If √(x) -1/(√(x))=√(7) , then find the value of x² + 1/(x²) .

If √(x) -1/(√(x))=√(7) , then find the value of x² +…

If $\sqrt{x} -\frac{1}{\sqrt{x}}=\sqrt{7}$ , then find the value of $x^2 + \frac{1}{x^2}$ .

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 79.

$\sqrt{x} -\frac{1}{\sqrt{x}}=\sqrt{7}$

on squaring both sides we get,

⇒ x + 1/x - 2 = 7

⇒ x + 1/x = 9

on squaring both sides we get,

⇒ x² + 1/x² + 2 = 81

⇒ x² + 1/x² = 79