Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x+\frac{1}{x}=3$, then the value of $x^2+\frac{1}{x^2}$ is

Options:

9

11

7

3

Correct Answer:

7

Explanation:

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

$⇒(3)^2=x^2+\frac{1}{x^2}+2$

$9=x^2+\frac{1}{x^2}+2$

$⇒x^2+\frac{1}{x^2}=9-2=7$