If 1/x+x=4 , then find 1/(x²)+x²

SSC CGL 2023 PYQ — Question 1

If $\frac{1}{x}+x=4$ , then find $\frac{1}{x^2}+x^2$

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 14

Given that

$\frac{1}{x}+x=4$

Square on both sides

$\frac{1}{x^2}+x^2$ + 2 = 16

$\frac{1}{x^2}+x^2$ = 16 - 2 = 14