Question

if x= 7+4√3 ,find the value of x^2 +1/x^2​

Answer 1

Answer:-

$\tt{x=7+4\sqrt{3}}$

Find:- $\tt{{x}^{2}+\dfrac{1}{{x}^{2}}}$

Putting the values,

$\leadsto\tt{{(7+4\sqrt{3})}^{2}+\dfrac{1}{{(7+4\sqrt{3})}^{2}}}$

$\leadsto\tt{(49+48+56\sqrt{3})+\dfrac{1}{(49+48+56\sqrt{3})}}$

$\leadsto\tt{(91+56\sqrt{3})+\dfrac{1}{(91+56\sqrt{3})}}$

$\leadsto\tt{(91+56\sqrt{3})+{(91+56\sqrt{3})}^{-1}}$

$\leadsto\tt{2\times{(91+56\sqrt{3})}^{-1}}$

$\leadsto\bf{{(182+112\sqrt{3})}^{-1}}$

$\rule{200}2$