If x = 1/(x-5) (x > 0),then the value of x + frac1 x is :

If $x = \frac{1}{x-5}$ (x > 0),then the value of $x + \frac1 x$ is :

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\sqrt29$ .

Given that

If $x = \frac{1}{x-5}$ (x > 0),

⇒ x - 5 = 1/x

⇒ x - 1/x = 5

Square both side

⇒ x²+ 1/x² -2 = 25

⇒ x²+ 1/x² = 25 + 2 = 27

⇒ (x + 1/x)² - 2 = 27

⇒ (x + 1/x)²= 29

⇒ x + 1/x = $\sqrt29$

SSC CHSL 2023 PYQ — Question 70