If x = 3 + 2√2, what is the value of √x - (1/√x)?

Question 34: If x = 3 + 2√2, what is the value of √x - (1/√x)?

Solution:
দেওয়া আছে,
x = 3 + 2√2
⇒ x = 2 + 2√2 + 1
⇒ x = (√2)² + 2√2 + 1²
⇒ x = (√2 + 1)²
∴ √x = √2 + 1

এখন,
1/√x = 1/(√2 + 1)
= (√2 - 1)/[(√2 + 1)(√2 - 1)]
= (√2 - 1)/(2 - 1)
= √2 - 1

সুতরাং, √x - (1/√x)
= (√2 + 1) - (√2 - 1)
= √2 + 1 - √2 + 1
= 2

∴ সঠিক উত্তর: খ) 2