Question

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

Answer 1

${ \textbf{ \huge{We \:have, }}}$

${ \boxed{ \boxed{ \blue{ \large{x = 2 - \sqrt{3} }}}}} \\ \\ { \boxed{ \boxed{ \blue{ \large{ \frac{1}{x} = > \frac{1}{2 - \sqrt{3} } = > > { \boxed{ \purple{2 + \sqrt{3}}}}}}}}}$

${ \text{ \huge{{Now, }}}}$

${ \large{x + \frac{1}{x} =(2 - \sqrt{3} ) + (2 + \sqrt{3} ) }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \large{2 - \sqrt{3} + 2 + \sqrt{3} }}\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \large{ \red{4}}}$

${ \text{ \huge{And, </p><p>}}}$

${ \large{{x}^{2} + \frac{1}{ {x}^{2} } = {(x + \frac{1}{x} )}^{2} - 2 }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \large{ {(4)}^{2} - 2}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \large{16 - 2 ={ \red{ 14}}}}$

${ \huge{ \textbf{Hence, }}}</p><p></p><p>$

${ \huge{ \boxed{ \boxed{{{x}^{2} + \frac{1}{ {x}^{2} } = 14}}}}} \\ \\ { \huge{ \boxed{ \boxed{{x + \frac{1}{x} = 4}}}}}$