Question

if x=3+2root2then find the value of x2+ 1 by 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=3+2√2
(x^2+1)/x^2=((3+2√2)^2)+1)/(3+2√2)^2
(9+8+12√2+1)/17+12√2
(18+12√2)/17+12√2