Answer:

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

Verified answer

Answer:

(3+2√2)² + 1/(3+2√2)²

9 + 8 + 12√2 + 1

____

9 + 8 + 12√2

17 + 12√2 + 1

______

17 + 12√2

289 + 288 + 408√2 + 1

____________________

17 + 2√2

578 + 408√2

__________

17 + 12√2