Question

please give the answer fast

Answer 1

$x = 2 + \sqrt{3} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{1} \\ \\ {x}^{2} = {(2 + \sqrt{3} )}^{2} \\ = 4 + 3 + 4 \sqrt{3} \\ \\ { (\frac{1}{x} )}^{2} = {(2 - \sqrt{3)}) }^{2} \\ = 4 + 3 - 4 \sqrt{3} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 4 + 3 - 4 \sqrt{3} + 4 + 3 + 4 \sqrt{3} \\ = 14ans.$

Answer 2

Hey, this is the answer!!!!!

If x=2+root 3
then 1/x =2- root 3 (by rationalisation)
then (x+1x)^2=x^2+(1/x)^2+2*x*(1/x)
i.e (2+ root 3 + 2- root 3)^2=x^2+(1/x)^2+2
4^2-2 =x^2 +(1/x)^2
i.e 14 is the answer.

Hope that this ans will help u!!!!