Difference between revisions of "Mathematical formula"

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

[Expand]\scriptstyle\sqrt{3}+\sqrt{12}


[Expand]\scriptstyle\sqrt{6}+\sqrt{7}


[Expand]\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)


[Expand]\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)


[Expand]\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}


Subtraction of Roots

[Expand]\scriptstyle\sqrt{12}-\sqrt{3}


[Expand]\scriptstyle\sqrt{7}-\sqrt{6}


[Expand]\scriptstyle19-\left(10-\sqrt{12}\right)


[Expand]\scriptstyle10-\left(24-\sqrt{250}\right)


[Expand]\scriptstyle16-\left(8+\sqrt{50}\right)


[Expand]\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)


Multiplication of Roots

[Expand]\scriptstyle\sqrt{4}\times\sqrt{9}


[Expand]\scriptstyle\sqrt{6}\times3


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)


[Expand]\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)


[Expand]\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)


[Expand]\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)


[Expand]\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)


[Expand]\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)


[Expand]\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)


[Expand]\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)


[Expand]\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)


[Expand]\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)


[Expand]\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)


[Expand]\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)


[Expand]\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)


[Expand]\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)


[Expand]\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)


[Expand]\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)


[Expand]\scriptstyle3\times\sqrt{4}


[Expand]\scriptstyle3\times\sqrt[3]{8}


[Expand]\scriptstyle\sqrt{4}\times\sqrt[3]{8}


[Expand]\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}


Linear Equation

[Expand]\scriptstyle bx=\sqrt[3]{c}


[Expand]\scriptstyle c=\sqrt[3]{bx}



Quadratic Equation

[Expand]\scriptstyle ax^2=\sqrt[3]{c}


[Expand]\scriptstyle c=\sqrt[3]{ax^2}



Cubic Equation

[Expand]\scriptstyle ax^3=\sqrt[3]{c}


Biquadratic Equation

[Expand]\scriptstyle4\sdot\left(x^2+8\right)=x^4


[Expand]\scriptstyle c=ax^4+\sqrt{bx^4}


[Expand]\scriptstyle ax^4+bx^2=c


[Expand]\scriptstyle bx^2=ax^4+c


[Expand]\scriptstyle ax^4=bx^2+c
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