Question

a=3-2√2 find √a-1/√a​

Answer 1

Solution :-

a = 3 - 2√2

It can be written as

⇒ a = (√2)² + 1² - 2(√2)(1)

⇒ a = (√2 - 1)²

[ Because (x - y)² = x² + y² - 2xy ]

Now, √a - 1/√a

= √(√2 - 1)² - 1/√(√2 - 1)²

= √2 - 1 - 1/(√2 - 1)

= √2 - 1 - (√2 + 1)

[ Because,

1/(√2 - 1)

= 1/(√2 - 1) * (√2 + 1)/(√2 + 1)

= (√2 + 1)/(2 - 1) = √2 + 1 ]

= √2 - 1 - √2 - 1

= - 2

Therefore the value of √a - 1/√a is - 2.