Question

if x+1/x=6find x²+1/x²​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

$\star{\sf{ { \: \: \green{x + \frac{1}{x} = 6}}}}$

${\bf{\blue{\underline{Find:}}}}$

$\star{\sf{ { \: \: \green{ {x}^{2} + \frac{1}{ {x}^{2} } = ? }}}}$

${\bf{\blue{\underline{Now:}}}}$

Squaring both side,

$: \implies{\sf{ \bigg(x + \frac{1}{x} \bigg )^{2} = ( {6})^{2} }}$

$: \implies{\sf{ \bigg( {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times \frac{1}{x} \times x \bigg )= 36 }}$

$: \implies{\sf{ \bigg( {x}^{2} + \frac{1}{ {x}^{2} } + 2 \bigg )= 36 }}$

$: \implies{\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2 }}$

$: \implies \boxed{\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 34 }}$