Question

give the answer of the following​

Answer 1

Given: ${(x\:+\:\frac{1}{x})\:=\:4}$

${x\:+\:\frac{1}{x}\:=\:4}$ ( squaring both sides)

${{x}^{2}\:+\:2\:×\:\frac{1}{x}\:×\:x\:+\:{\frac{1}{x}}^{2}=\:{(4)}^{2}}$

${{x}^{2}\:+\:2\:+\:\frac{1}{{x}^{2}}=\:16}$

${{x}^{2}\:+\:2\:+\:\frac{1}{{x}^{2}}=\:16\:-\:2}$

$\large{\boxed{{\large{[{x}^{2}\:+\:\frac{1}{{x}^{2}}}}]\:=\:14}}$