Question

if x=3+2√2 , find the value of x^2 + 1/x^2​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

$x=3+2√2$

So

$\displaystyle \: \frac{1}{x} = \frac{1}{3+2√2 }$

$\implies \: \displaystyle \: \frac{ 1 }{x} = \frac{3 - 2√2 }{(3 + 2√2) (3 - 2√2)}$

$\implies \: \displaystyle \: \frac{ 1 }{x} = \frac{3 - 2√2 }{{3}^{2} - ({ 2√2})^{2} }$

$\implies \: \displaystyle \: \frac{ 1 }{x} = \frac{3 - 2√2 }{9 - 8}$

$\implies \: \displaystyle \: \frac{ 1 }{x} = {3 - 2√2 }$

So

$\displaystyle \: x + \frac{ 1 }{x} = {3 + 2√2 } + 3 + 2 \sqrt{2} = 6$

So

$\displaystyle \: {x}^{2} + \frac{1}{ {x}^{2} }$

$= \displaystyle \: {(x + \frac{1}{x} )}^{2} - 2 \times x \times \frac{1}{x}$

$= {6}^{2} - 2$

$= 36 - 2$

$= 34$