Difference between revisions of "Divide a Number Problems"

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== Divide Thirty into Two Parts ==
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<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">
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[[comment: a+b=30;a/b=27]]
 
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Revision as of 08:10, 2 March 2022

Divide Ten into Two Parts

[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=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\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}=5\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 a^2=9b\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\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}=3+\frac{3}{4}\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 a^2=\frac{1}{4}b\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\\\scriptstyle3a=b\sdot\sqrt{8}\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\\\scriptstyle b^2-a^2=80\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}=\frac{5}{6}\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\\\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\frac{b}{a}\sdot\left(b-a\right)=24\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\frac{a}{b}+\frac{b}{a}=\sqrt{5}\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\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\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}


Divide Thirty into Two Parts

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