Difference between revisions of "Divide a Number Problems"

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(→‎Divide Ten into Two Parts)
(→‎Divide Ten into Two Parts)
 
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<div class="mw-collapsible mw-collapsed">30 into 4 parts<div class="mw-collapsible-content">
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{{#annotask:
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[[category: #divide a number]]
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[[comment: 30 into 4 parts]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed">600 into 3 parts<div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: 600 into 3 parts]]
 +
}}</div></div>
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<br>
  
 
== Divide Ten into Two Parts ==
 
== Divide Ten into Two Parts ==
  
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, 3a=b√8]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, ab=21]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=24+\frac{3}{4}\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, ab=24+¾]]
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}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a²=9b]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a²=¼b]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(48+\frac{1}{6}\right)\sdot a\end{cases}</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b²=(48+⅙)a]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a²=4ab]]
+
[[comment: a+b=10, a²=4ab]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{5}\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a²=⅕ab]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a²=1½ab]]
+
[[comment: a+b=10, a²=1½ab]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{1}{3}\right)\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b²=(3+⅓)ab]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(2+\frac{1}{4}\right)\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b²=2¼a²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{22}{49}\right)\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b²=(3+²²/₄₉)a²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=4\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, 10²=4a²]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 10²=16a²]]
+
[[comment: a+b=10, 10²=16a²]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 10²=6¼a²]]
+
[[comment: a+b=10, 10²=6¼a²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b/a=4]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: b/a=5]]
+
[[comment: a+b=10, b/a=5]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a/b=6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=100\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a/b=100]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=\frac{1}{5}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: b/a=4]]
+
[[comment: a+b=10, a/b=⅕]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a²=9b]]
+
[[comment: a+b=10, a/b=4¼]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6+\frac{1}{3}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: ab=21]]
+
[[comment: a+b=10, a/b=6+⅓]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a/b+b/a=2⅙]]
+
[[comment: a+b=10, a/b+b/a=2⅙]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a/b+b/a=4¼]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a/b+b/a=√5]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, a/b-b/a=5/6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b/a-a/b=5/6]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a/b-b/a=3¾]]
+
[[comment: a+b=10, a/b-b/a=3¾]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, (b/a)·(b-a)=24]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: b²-a²=50]]
+
[[comment: a+b=10, b²-a²=50]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a²=¼b]]
+
[[comment: a+b=10, a²-b²=80]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (a-b)²=20+¼]]
+
[[comment: a+b=10, (a-b)²=20+¼]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b-a)²-a²=32]]
+
[[comment: a+b=10, (b-a)²-a²=32]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 3a=b√8]]
+
[[comment: a+b=10, (a-b)²·a=20¼a]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot b=\left(20+\frac{1}{4}\right)b\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (a-b)²·a=20¼a]]
+
[[comment: a+b=10, (a-b)²·b=20¼b]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (ab)·a=21a]]
+
[[comment: a+b=10, (ab)·a=21a]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (a-b)²·7⅑=(ab)²]]
+
[[comment: a+b=10, (a-b)²·7⅑=(ab)²]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (ab+a²)a=(a½a)²+36]]
+
[[comment: a+b=10, (ab+a²)a=(a½a)²+36]]
 +
}}</div></div>
 +
<br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, 6a+⅓[(6a)/b]=56]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, b/a+a=5½]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, (b/a+b)·a=30]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a²-b²=80]]
+
[[comment: a+b=10, (b/a)·b=9]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a/b+b/a=4¼]]
+
[[comment: a+b=10, (b/a)²·a=32]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a/b-b/a=5/6]]
+
[[comment: a+b=10, (a/b+b/a)·b=34]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a/b=4¼]]
+
[[comment: a+b=10, (b/a+10)·a=46]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 6a+⅓[(6a)/b]=56]]
+
[[comment: a+b=10, (b/a+10)·b=69]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: b/a+a=5½]]
+
[[comment: a+b=10, (a/b+b/a+10)·a=73]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a+b)·a=30]]
+
[[comment: a+b=10, (a/b-b/a)·a=5]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a)·b=9]]
+
[[comment: a+b=10, (a/b+b/a)·a=25-2a]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a)²·a=32]]
+
[[comment: a+b=10, (a/b+a)·(b/a+b)=35]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a)·(b-a)=24]]
+
[[comment: a+b=10, (b/a+10)·(a/b+10)=122⅔]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (a/b+b/a)·b=34]]
+
[[comment: a+b=10, (10+b/a)·(10-a/b)=107⅓]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a+10)·a=46]]
+
[[comment: a+b=10, (a·b)/(b-a)=√6]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (b/a+10)·b=69]]
+
[[comment: a+b=10, b²-(a·√8)=40]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
−
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}</math><div class="mw-collapsible-content">
+
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (a/b+b/a+10)·a=73]]
+
[[comment: a+b=10, a·√10=b²]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
  
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, (a/b)²+(b/a)²=3]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, (b/a)²-(a/b)²=2]]
 +
}}</div></div>
 +
<br>
  
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: a+2√a=b-2√b]]
+
[[comment: a+b=10, a+2√a=b-2√b]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 10/a+10/b=6¼]]
+
[[comment: a+b=10, 10/a+10/b=6¼]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 10/a·10/b=6¼]]
+
[[comment: a+b=10, 10/a·10/b=6¼]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 40/a·40/b=100]]
+
[[comment: a+b=10, 40/a·40/b=100]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: 50/a·40/b=125]]
+
[[comment: a+b=10, 50/a·40/b=125]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (10/a·10/b)²=20¼]]
+
[[comment: a+b=10, (10/a·10/b)²=20¼]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into two parts]]
+
[[category: #divide a number]]
−
[[comment: (40/a)²·(40/b)²=625]]
+
[[comment: a+b=10, (40/a)²·(40/b)²=625]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50-b=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10,20+a=n²,50-b=m²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50+b=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=10, 20+a=n²,50+b=m²]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Eleven into Two Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=11\\\scriptstyle\frac{1}{2}a+\frac{1}{4}a=\frac{1}{3}b+\frac{1}{5}b\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=11, ½a+¼a=⅓b+⅕b]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Twenty into Two Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=20\\\scriptstyle b=4a\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=20, b=4a]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Twenty-Four into Two Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=24\\\scriptstyle\frac{2}{3}a+\frac{3}{4}b=a\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=24, ⅔a+¾b=a]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Thirty into Two Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle\frac{a}{b}=27\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=30;a/b=27]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle4a=3b\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b=30, 4a=3b]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 249: Line 460:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
−
[[category: #divide 10 into three parts]]
+
[[category: #divide a number]]
−
[[comment: a^2+b^2=c^2, ac=b^2]]
+
[[comment: a+b+c=10, a^2+b^2=c^2, ac=b^2]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Eighteen into Three Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b+c=18\\\scriptstyle a-\frac{1}{5}a=b+\frac{1}{3}b=c\sdot\left(2+\frac{1}{2}\right)\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b+c=18, a-⅕a=b+⅓b=2½c]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Twenty-Seven into Three Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^3+b^3+c^3=27</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a³+b³+c³=27]]
 +
}}</div></div>
 +
<br>
 +
 
 +
== Divide Thirty into Three Parts ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b+c=30\\\scriptstyle7a=\frac{b}{5}=\frac{c}{10}\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #divide a number]]
 +
[[comment: a+b+c=30, 7a=b/5=c/10]]
 
}}</div></div>
 
}}</div></div>
 +
<br>

Latest revision as of 17:47, 1 May 2023

[Expand]30 into 4 parts


[Expand]600 into 3 parts


Divide Ten into Two Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=24+\frac{3}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(48+\frac{1}{6}\right)\sdot a\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{5}\sdot\left(a\sdot b\right)\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{1}{3}\right)\sdot\left(a\sdot b\right)\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(2+\frac{1}{4}\right)\sdot a^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2=\left(3+\frac{22}{49}\right)\sdot a^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=4\sdot a^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=100\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=\frac{1}{5}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=6+\frac{1}{3}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot b=\left(20+\frac{1}{4}\right)b\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50-b=m^2\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle20+a=n^2\\\scriptstyle50+b=m^2\end{cases}


Divide Eleven into Two Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=11\\\scriptstyle\frac{1}{2}a+\frac{1}{4}a=\frac{1}{3}b+\frac{1}{5}b\end{cases}


Divide Twenty into Two Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=20\\\scriptstyle b=4a\end{cases}


Divide Twenty-Four into Two Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=24\\\scriptstyle\frac{2}{3}a+\frac{3}{4}b=a\end{cases}


Divide Thirty into Two Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle\frac{a}{b}=27\end{cases}


[Expand]\scriptstyle\begin{cases}\scriptstyle a+b=30\\\scriptstyle4a=3b\end{cases}


Divide Ten into Three Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}


Divide Eighteen into Three Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b+c=18\\\scriptstyle a-\frac{1}{5}a=b+\frac{1}{3}b=c\sdot\left(2+\frac{1}{2}\right)\end{cases}


Divide Twenty-Seven into Three Parts

[Expand]\scriptstyle a^3+b^3+c^3=27


Divide Thirty into Three Parts

[Expand]\scriptstyle\begin{cases}\scriptstyle a+b+c=30\\\scriptstyle7a=\frac{b}{5}=\frac{c}{10}\end{cases}


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