Question

If x =3+2√2 then. find the value of (x-1/x) 3

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Answer 1

Step-by-step explanation:

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Answer 2

$\rm If \ x = 3+2\surd{2} \ \ then,\dfrac{1}{x}= \dfrac{1}{3+2\surd{2}}$

Rationalising $\rm \dfrac{1}{3+2\sqrt{2}}$

$\sf \implies\dfrac{1}{3+2\sqrt{2}} \times \dfrac{3 - 2\sqrt{2}}{3-2\sqrt{2}} \implies\dfrac{3 - 2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})}$

$\Rightarrow\sf \dfrac{3-2\sqrt{2}}{(3)^2-(2\sqrt{2})^2} = \dfrac{3-2\sqrt{2}}{9-8}$

$\sf \mapsto \dfrac{3-2\sqrt{2}}{1} = 3-2\sqrt{2}$

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Now we will find $\rm \Bigg ( x-\dfrac{1}{x} \Bigg )^3$

Substituting the values of $\rm x \ and \ \dfrac{1}{x}$ will give

$\implies \rm [ 3+2\sqrt{2}-(3-2\sqrt{2})]^3$

$\implies \rm (3+2\sqrt{2}-3+2\sqrt{2})^3$

$\implies \rm ( 2\sqrt{2}+2\sqrt{2})^3$

$\implies \rm (4\sqrt{2})^3$

$\implies \rm 128\sqrt{2}$

Therefore, the value of (x-1/x)³ is 128√2

Hope it helps .