Difference between revisions of "Mathematical formula"

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[[(3n+1)²=((10·(⅓·3n)²)-(⅓·3n)²)+3n+(3n+1)|
 
[[(3n+1)²=((10·(⅓·3n)²)-(⅓·3n)²)+3n+(3n+1)|
 
<math>\scriptstyle\left(3n+1\right)^2=\left[\left[10\sdot\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]-\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]+3n+\left(3n+1\right)</math>]]
 
<math>\scriptstyle\left(3n+1\right)^2=\left[\left[10\sdot\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]-\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]+3n+\left(3n+1\right)</math>]]
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 +
== Roots ==
 +
 +
 +
=== Multiplication of Roots ===
  
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">
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[[category: #R×(N-R)]]
 
[[category: #R×(N-R)]]
 
[[comment: √3×(6-√8)]]
 
[[comment: √3×(6-√8)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)×(N+R)]]
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[[comment: (3+√5)×(3+√5)]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)×(N+R)]]
 +
[[comment: (3+√5)×(4+√7)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)×(N+R)]]
 +
[[comment: (3+√4)×(4+√9)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N-R)×(N-R)]]
 +
[[comment: (3-√5)×(4-√7)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N-R)×(N-R)]]
 +
[[comment: (3-√5)×(3-√5)]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)×(N-R)]]
 +
[[comment: (5+√3)×(5-√3)]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)×(N-R)]]
 +
[[comment: (3+√4)×(5-√9)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R×(R-N)]]
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[[comment: √8×(√8-2)]]
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}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R-N)×(R-N)]]
 +
[[comment: (√8-2)×(√10-3)]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R-N)×(R-N)]]
 +
[[comment: (√12-2)×(√12-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R-N)×(R+N)]]
 +
[[comment: (√15-3)×(√12+2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R+N)×(R-N)]]
 +
[[comment: (√8+2)×(√8-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R×(R+R)]]
 +
[[comment: √5×(√7+√10)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R×(R-R)]]
 +
[[comment: √5×(√12-√8)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R+R)×(R+R)]]
 +
[[comment: (√5+√7)×(√10+√15)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R+R)×(R+R)]]
 +
[[comment: (√5+√7)×(√5+√7)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R+R)×(R-R)]]
 +
[[comment: (√5+√7)×(√10-√6)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R+R)×(R-R)]]
 +
[[comment: (√10+√7)×(√10-√7)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(R-R)×(R-R)]]
 +
[[comment: (√12-√7)×(√15-√10)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>

Revision as of 14:30, 16 April 2019


\scriptstyle\left(3n+1\right)^2=\left[\left[10\sdot\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]-\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]+3n+\left(3n+1\right)

Roots

Multiplication of Roots

\scriptstyle\sqrt{4}\times\sqrt{9}
no such category found: #R×R


\scriptstyle\sqrt{6}\times3
no such category found: #R×N


\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)
no such category found: #R×(R+N)


\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)
no such category found: #R×(N-R)


\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)
no such category found: #(N+R)×(N+R)


\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)
no such category found: #(N+R)×(N+R)


\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)
no such category found: #(N+R)×(N+R)


\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)
no such category found: #(N-R)×(N-R)


\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)
no such category found: #(N-R)×(N-R)


\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)
no such category found: #(N+R)×(N-R)


\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)
no such category found: #(N+R)×(N-R)


\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)
no such category found: #R×(R-N)


\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)
no such category found: #(R-N)×(R-N)


\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)
no such category found: #(R-N)×(R-N)


\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)
no such category found: #(R-N)×(R+N)


\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)
no such category found: #(R+N)×(R-N)


\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)
no such category found: #R×(R+R)


\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)
no such category found: #R×(R-R)


\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)
no such category found: #(R+R)×(R+R)


\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)
no such category found: #(R+R)×(R+R)


\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)
no such category found: #(R+R)×(R-R)


\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)
no such category found: #(R+R)×(R-R)


\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)
no such category found: #(R-R)×(R-R)


\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)
no such category found: #(R-R)×(R-R)


\scriptstyle3\times\sqrt{4}
no such category found: #N×R


\scriptstyle3\times\sqrt[3]{8}
no such category found: #N×R₃


\scriptstyle\sqrt{4}\times\sqrt[3]{8}
no such category found: #R×R₃


\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}
no such category found: #R₃×R₄


Linear Equation

\scriptstyle bx=\sqrt[3]{c}
Category Comment Link Annotated text
equation/linear equationbx=³√cספר_ג'יבלי_אלמוקבאלא#NHZdWhen things are equal to a cube root of the numbers: :\scriptstyle bx=\sqrt[3]{c} כאשר הדברי' יהיו שוי' אל שרש מעוק' ממספרי‫'


\scriptstyle c=\sqrt[3]{bx}
Category Comment Link Annotated text
equation/linear equationc=³√bxספר_ג'יבלי_אלמוקבאלא#jGFmWhen numbers are equal to a cube root of a thing: :\scriptstyle c=\sqrt[3]{bx} כאשר המספרי' יהיו שוים אל שרש מעו' מדבר



Quadratic Equation

\scriptstyle ax^2=\sqrt[3]{c}
Category Comment Link Annotated text
equation/quadratic equationax²=³√cספר_ג'יבלי_אלמוקבאלא#rGD5When squares are equal to a cube root of the numbers: :\scriptstyle ax^2=\sqrt[3]{c} כאשר הצינסי יהיו שוים אל שרשי' מעו' ממספרי‫'


\scriptstyle c=\sqrt[3]{ax^2}
Category Comment Link Annotated text
equation/quadratic equationc=³√ax²ספר_ג'יבלי_אלמוקבאלא#zK2yWhen numbers are equal to a cube root of squares: :\scriptstyle c=\sqrt[3]{ax^2} כאשר המספרי' יהיו שוים אל שרשי' מעו' מצינסי



Cubic Equation

\scriptstyle ax^3=\sqrt[3]{c}
Category Comment Link Annotated text
equation/cubic equationax³=³√cספר_ג'יבלי_אלמוקבאלא#eOI5It is when cubes are equal to a cube root of the numbers: :\scriptstyle ax^3=\sqrt[3]{c} וזהו כאשר המעוקבי' יהיו שוים אל שרש מעו' ממספרי‫'


Biquadratic Equation

\scriptstyle4\sdot\left(x^2+8\right)=x^4
Category Comment Link Annotated text
quartic equation/biquadratic equation4(x²+8)=x⁴אגרת_המספר#q2Fw6) \scriptstyle4\sdot\left(x^2+8\right)=\left(x^2\right)^2 הששית ממון הוספת עליו ח' זוזים והכית המקובץ בארבעה והיה היוצא הכאת הממון בעצמו
quartic equation/biquadratic equation4(x²+8)=x⁴תחבולות_המספר#G1Mq[6] He said: the six problem is as if you are told: we add to a certain square [eight] dirham, then multiply the sum by four dirham and the result is the same as the product of the square [by itself]. :\scriptstyle4\sdot\left(X^2+8\right)=\left(X^2\right)^2 אמ' והשאלה הששית כמו אם יאמרו לך הוספנו על התמונ' מרובע מה שלשה דרהמי והכינו המקובץ בארבעה דרהמי והיה העולה כמו הכאת א"ב בעצמו המרובע
quartic equation/biquadratic equation4(x²+8)=x⁴חשבון_השטחים#ZxMx\scriptstyle4\sdot\left(X^2+8\right)=\left(X^2\right)^2 אלגו תוסיף עליו שמנה אדרהם ותכה {{#annot:term|388,1217|vQSL}}המקובץ{{#annotend:vQSL}} על ארבעה אדרהם והיה כמו האלגו על עצמו


\scriptstyle c=ax^4+\sqrt{bx^4}
Category Comment Link Annotated text
quartic equation/biquadratic equationc=ax⁴+√(bx⁴)ספר_ג'יבלי_אלמוקבאלא#h9ilWhen numbers are equal to squares of squares and a root of squares of squares: :\scriptstyle c=ax^4+\sqrt{bx^4} כאשר המספרי' יהיו שוים אל הצינסי מצינסי ואל שרשי צינסי מצינסי


\scriptstyle ax^4+bx^2=c
Category Comment Link Annotated text
quartic equation/biquadratic equationax⁴+bx²=cספר_ג'יבלי_אלמוקבאלא#Tu7NWhen squares of squares plus squares are equal to a number: :\scriptstyle ax^4+bx^2=c כאשר הצינסי מצינסי וצינסי יהיו שוים אל מספר


\scriptstyle bx^2=ax^4+c
Category Comment Link Annotated text
quartic equation/biquadratic equationbx²=ax⁴+cספר_ג'יבלי_אלמוקבאלא#tkSOWhen squares are equal to squares of squares and a root of a number: :\scriptstyle bx^2=ax^4+c כאשר הצינסי יהיו שוים אל הצינסי מצינסי ואל מספר


\scriptstyle ax^4=bx^2+c
Category Comment Link Annotated text
quartic equation/biquadratic equationax⁴=bx²+cספר_ג'יבלי_אלמוקבאלא#CLbnWhen squares of squares are equal to a number and squares: :\scriptstyle ax^4=bx^2+c כאשר הצינסי מצינסי יהיו שוים אל המספר והצינסי
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