Question

If x=3 + 2√2,

Then find x² + 1/x²

Answer 1

Given x = 3 + 2√2

(3+2√2)^2= 17+12√2

⇒ x^2 = 17 + 12√2

⇒ 1/x2 = 1/(17 + 12√2)

On rationalizing the denominator we get
1/x2 = (17 – 12√2)
∴ (x2 +1/x2) =
(17 + 12√2) + (17 – 12√2)
= 34