Difference between revisions of "Mathematical formula"

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== Roots ==
 
== Roots ==
  
 +
 +
=== Addition of Roots ===
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R+R]]
 +
[[comment: √3+√12]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R+R]]
 +
[[comment: √6+√7]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)+(N+R)]]
 +
[[comment: (4+√12)+(5+√3)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)+(R-N)]]
 +
[[comment: (4+√3)+(√12-3)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N+R)+(R-N)]]
 +
[[comment: (4+√3)+(√12-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N-R)+(R-N)]]
 +
[[comment: (4-√3)+(√12-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R+R+R+R]]
 +
[[comment: √3+√6+√12+√24]]
 +
}}</div></div>
 +
<br>
 +
 +
=== Subtraction of Roots ===
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R-R]]
 +
[[comment: √12-√3]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R-R]]
 +
[[comment: √7-√6]]
 +
}}</div></div>
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<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #N-(N-R)]]
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[[comment: 19-(10-√12)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #N-(N-R)]]
 +
[[comment: 10-(24-√250)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #N-(N+R)]]
 +
[[comment: 16-(8+√50)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #(N-R)-(N-R)]]
 +
[[comment: (13-√20)-(6-√5)]]
 +
}}</div></div>
 +
<br>
  
 
=== Multiplication of Roots ===
 
=== Multiplication of Roots ===

Revision as of 19:51, 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

Addition of Roots

\scriptstyle\sqrt{3}+\sqrt{12}
no such category found: #R+R


\scriptstyle\sqrt{6}+\sqrt{7}
no such category found: #R+R


\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)
no such category found: #(N+R)+(N+R)


\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)
no such category found: #(N+R)+(R-N)


\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)
no such category found: #(N+R)+(R-N)


\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)
no such category found: #(N-R)+(R-N)


\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}
no such category found: #R+R+R+R


Subtraction of Roots

\scriptstyle\sqrt{12}-\sqrt{3}
no such category found: #R-R


\scriptstyle\sqrt{7}-\sqrt{6}
no such category found: #R-R


\scriptstyle19-\left(10-\sqrt{12}\right)
no such category found: #N-(N-R)


\scriptstyle10-\left(24-\sqrt{250}\right)
no such category found: #N-(N-R)


\scriptstyle16-\left(8+\sqrt{50}\right)
no such category found: #N-(N+R)


\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)
no such category found: #(N-R)-(N-R)


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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