​ If x = √6 + √5, then x^2 + 1/x^2 - 2 = A. 2√6 B. 2√5 C. 24 D. 20 ​

Question

If x = √6 + √5, then x² + \(\frac{1}{x^2}\) -2 = 

A. 2√6

B. 2√5

C. 24

D. 20

Answer 1

Given x= √6 + √5

X² = 11 + 2√11

\(\frac{1}{x^2}\) = 11- 2√11

So, x² +\(\frac{1}{x^2}\) – 2 = 11+ 2√11 + 11 – 2√11 -2 = 22 - 2 = 20.