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

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Solution

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

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