Question

If $x+x^{-1}=10,(x\ne 0)$ then evaluate :
$x^2+x^{-2}$.

• A. 102
• B. 98
• C. 10
• D. 100

Answer 1

The correct option is B 98

$(x+x^{-1}{)}^2=(10{)}^2$

Squaring both sides,

$x^2+x^{-2}+2\left(x\right)\left(x^{-1}\right)=100$

$x^2+x^{-2}+2=100$

$x^2+x^{-2}=100-2$

$x^2+x^{-2}=98$