Question

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

• A. 119
• B. 120
• C. 121
• D. 122

Answer 1

The correct option is A 119

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

$({x+x^{-1})}^2={11}^2$ [Squaring both the sides]

$\Rightarrow {\left(x\right)}^2+{\left(x^{-1}\right)}^2+2\left(x\right)\left(x^{-1}\right)=121$

$\Rightarrow x^2+x^{-2}+2=121$ $[\because (x)\left(x^{-1}\right)=x^0=1]$

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