Question

If $x+x^{-1}=11$, evaluate $x^2+x^{-2}$.

• A. 119
• B. 120
• C. 122
• D. 121

Answer 1

The correct option is A

119

$x+x^{-1}=11$

$({x+x^{-1})}^2$ = ${\left(x\right)}^2+{\left(x^{-1}\right)}^2+2\left(x\right)\left(x^{-1}\right)={11}^2$

$\Rightarrow x^2+x^{-2}+2=121$

$\Rightarrow x^2+x^{-2}=121-2=119$