Question

If $(x+\frac{1}{x})=5$, then $(x^2+\frac{1}{x^2})$ is equal to

• A. 20
• B. 24
• C. 27
• D. 23

Answer 1

The correct option is D 23

Given,$x+\frac{1}{x}=5$
On squaring both sides, we get
$x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}=25$
$\Rightarrow x^2+\frac{1}{x^2}+2=25$
$\Rightarrow x^2+\frac{1}{x^2}=23$
Option D is correct.