Question

if x = 3+2√2 then find the value of (x+1/x )^3​

Answer 1

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Answer 2

Answer:

216.

Step-by-step explanation:

Given :

$\large x=3+2\sqrt2$

Now taking reciprocal of both side

$\large \dfrac{1}{x}=\dfrac{1}{3+2\sqrt2}$

Now rationalize the denominator

$\large \dfrac{1}{x}=\dfrac{1}{3+2\sqrt2}\times\dfrac{3-2\sqrt2}{3-2\sqrt2} \\\\\\\large \dfrac{1}{x}=\dfrac{3-2\sqrt2}{9-8}\\\\\\\large \dfrac{1}{x}=\dfrac{3-2\sqrt2}{1}\\\\\\\large \dfrac{1}{x}= 3-2\sqrt2$

Now adding both

$\large x+\dfrac{1}{x}= 3+2\sqrt2+3-2\sqrt2\\\\\\\large x+\dfrac{1}{x}= 3+3\\\\\\\large x+\dfrac{1}{x}= 6$

We have to find  $\large (x+\dfrac{1}{x})^3$

Putting value here we get

$\large \text{ (x+\dfrac{1}{x})^3 We can also write as }\\\\\\\large \text{ (x+\dfrac{1}{x})^3=(x+\dfrac{1}{x})(x+\dfrac{1}{x})(x+\dfrac{1}{x}) Put value }\\\\\\\large (x+\dfrac{1}{x})^3=6\times6\times6\\\\\\\large (x+\dfrac{1}{x})^3=216$

Thus we get answer.