Question

If x=3-2√2 find the value of (√x-1/√x)

Answer 1

Answer:√x + (1/√x) = (√2 – 1) + (√2 + 1) = 2√2

Step-by-step explanation:

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