Question

If x=3+2✓2 find ✓x+1/✓x

Answer 1

Given x = 3 – 2√2
⇒ x = 2 + 1 – 2√2
⇒ x = (√2)2 + 12 – 2 × √2 × 1
⇒ x = (√2 – 1 )2
∴ √x = (√2 – 1 )
Now consider, (1/√x) = 1/(√2 – 1 )
Multiply and divide with (√2 + 1 ), we get
(1/√x) = (√2 + 1 )/[(√2 – 1 )(√2 + 1 )]
          = (√2 + 1 )/[2 – 1]
∴  (1/√x) = (√2 + 1 )
√x + (1/√x) = (√2 – 1) + (√2 + 1) = 2√2