Question

if x=7+5√2,then(x^2+1/x^)​

Answer 1

$\huge \mathcal{\underline{\underline{GIVEN : \: \:\: \:\: \:\: \:\: \:}}}$

$\boxed{ \bf x = 7 + 5 \sqrt{2}}$

$\huge \mathcal{\underline{\underline{TO \: \: FIND \: :\: \:}}}$

$\boxed{\sf {x}^{2} + \frac{1}{ {x}^{2} } }$

$\huge \mathcal{\underline{\underline{SOLUTION :}}}$

$\huge = > {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ = > \frak{{(7 + 5 \sqrt{2})}^{2} + \frac{1}{{(7 + 5 \sqrt{2})}^{2} } } \\ \\ = > \frak{(49 + 50 + 70 \sqrt{2} ) + \frac{1}{49 + 50 + 70 \sqrt{2} }} \\ \\ = > \frak{99 + 70 \sqrt{2} + \frac{1}{99 + 70 \sqrt{2} }} \\ \\ = > \frak{99 \cancel{+ 70 \sqrt{2}} + {99 \cancel{- 70 \sqrt{2}} }{} } \\ \\ = > \frak{99 +99} = \sf{\red{198}}$