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 ==
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 +
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=== 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)]]
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}}</div></div>
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<br>
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<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">
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{{#annotask:
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[[category: #(N+R)×(N+R)]]
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[[comment: (3+√5)×(3+√5)]]
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}}</div></div>
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<br>
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<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">
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{{#annotask:
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[[category: #(N+R)×(N+R)]]
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[[comment: (3+√5)×(4+√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(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #(N+R)×(N+R)]]
 +
[[comment: (3+√4)×(4+√9)]]
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}}</div></div>
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<br>
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<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">
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{{#annotask:
 +
[[category: #(N-R)×(N-R)]]
 +
[[comment: (3-√5)×(4-√7)]]
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}}</div></div>
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<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">
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{{#annotask:
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[[category: #(N-R)×(N-R)]]
 +
[[comment: (3-√5)×(3-√5)]]
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}}</div></div>
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<br>
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<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">
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{{#annotask:
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[[category: #(N+R)×(N-R)]]
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[[comment: (5+√3)×(5-√3)]]
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}}</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)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #R×(R-N)]]
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[[comment: √8×(√8-2)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #(R-N)×(R-N)]]
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[[comment: (√8-2)×(√10-3)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #(R-N)×(R-N)]]
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[[comment: (√12-2)×(√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(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #(R-N)×(R+N)]]
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[[comment: (√15-3)×(√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(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #(R+N)×(R-N)]]
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[[comment: (√8+2)×(√8-2)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content">
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{{#annotask:
 +
[[category: #R×(R+R)]]
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[[comment: √5×(√7+√10)]]
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}}</div></div>
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<br>
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #R×(R-R)]]
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[[comment: √5×(√12-√8)]]
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}}</div></div>
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<br>
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<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

[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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