Question

if x= 3+2√2 , find x²+1/x²

Answer 1

Given x = 3 + 2√2
⇒ x2 = 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

Answer 2

x^2+ 1/x^2 = (3+2√2)^2+1/(3+2√2)2
(9+4×2)+1/(9+4×2)= 17+1/17 = 289+1/17=290/17=17.05