Question

If $(x-\frac{1}{x})=5$, then find the value of $(x^2+\frac{1}{x^2})$.

• A. $32$
• B. $15$
• C. $27$
• D. $11$

Answer 1

The correct option is C $27$

$x-\frac{1}{x}=5$

Squaring both sides,

$={(x-\frac{1}{x})}^2=5^2$

$=x^2+{\left(\frac{1}{x}\right)}^2-2\left(x\right)\left(\frac{1}{x}\right)=25$

$=x^2+\frac{1}{x^2}-2=25$

$=x^2+\frac{1}{x^2}=27$