If x (5 - 2/x ) = 5/x , then the value of x² + 1/(x²) is:

If x (5 - $\frac{2}{x}$ ) = $\frac{5}{x}$ , then the value of x² + $\frac{1}{x^2}$ is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{54}{25}$ .

Given that

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

⇒ 5x - 2 = $\frac{5}{x}$

⇒ 5(x - $\frac{1}{x}$ ) = 2

⇒ x - $\frac{1}{x}$ = 2/5

Square both sides

⇒ x² + $\frac{1}{x^2}$ = 4/25 + 2 = 54/25

SSC CPO 2023 PYQ — Question 135