If a = 1/(a-sqrt6) (a > 0), then the value of (a+1/a) is:

If a = $\frac{1}{a-\sqrt6}$ (a > 0), then the value of $(a+\frac 1 a)$ is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\sqrt 10$ .

Given that

If a = $\frac{1}{a-\sqrt6}$ (a > 0)

⇒ a - √6 = 1/a

⇒ a - 1/a = √6

Square both side

⇒ a²+ 1/a² - 2 = 6

⇒ a²+ 1/a² = 6 + 2 = 8

⇒ (a + 1/a)² - 2 = 8

⇒ (a + 1/a)²= 10

⇒ a + 1/a = $\sqrt 10$

SSC CHSL 2023 PYQ — Question 68