√(3+2√2)

√(3 -2√2)

x=3+2√2

then find the value of √x-√1/x

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Solution

Answer : 2
Given x = 3 + 2√2

⇒ x = 2 + 1 + 2√2 × 1

⇒ x = (√2)² + 1² + 2 × √2 × 1 We know (a + b)² = a² + b² + 2ab

⇒ 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

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