Question-155692

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Question Number 155692 by cortano last updated on 03/Oct/21

Commented by cortano last updated on 03/Oct/21

$$\mathrm{why}\:\mathrm{a}^{\mathrm{2}} =\:\mathrm{x}\left(\mathrm{2x}\right)? \\ $$

Commented by amin96 last updated on 03/Oct/21

$$ \\ $$

Commented by amin96 last updated on 03/Oct/21

a^2 =x(x+x)=2x^2 ⇒ a=x(√2) (3x)^2 −a^2 =b^2 ⇒ b^2 =7x^2 b=x(√7) cot(𝚿)=(b/a)=((x(√7))/(x(√2)))=(√(3,5))

$$\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{x}}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\:\Rightarrow\:\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{x}}\sqrt{\mathrm{2}} \\ $$$$\left(\mathrm{3}\boldsymbol{\mathrm{x}}\right)^{\mathrm{2}} −\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\boldsymbol{\mathrm{b}}^{\mathrm{2}} \:\:\:\Rightarrow\:\:\:\boldsymbol{\mathrm{b}}^{\mathrm{2}} =\mathrm{7}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{x}}\sqrt{\mathrm{7}} \\ $$$$\boldsymbol{\mathrm{cot}}\left(\boldsymbol{\Psi}\right)=\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}=\frac{\boldsymbol{\mathrm{x}}\sqrt{\mathrm{7}}}{\boldsymbol{\mathrm{x}}\sqrt{\mathrm{2}}}=\sqrt{\mathrm{3},\mathrm{5}} \\ $$

Commented by amin96 last updated on 03/Oct/21