Question

1
. If x = 3 + 2 root2, find the value of (rootx -1upon rootx ) ​

Answer 1

Answer:

HOPE YOU WILL UNDERSTAND THE SOLUTION.

Answer 2

Given that,

x = 3 + 2√2

To find: Value of √x - 1/√x.

Here,

x = 3 + 2√2 = 2 + 2√2 + 1

⇒ x = (√2)² + (1)² + 2(√2)(1)

⇒ x = (√2 + 1)² {by (a + b)² identity}

⇒ √x = √2 + 1.

Now, 1/√x = 1/(√2 + 1)

By rationalising the denominator,

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

⇒ 1/√x = √2 - 1

So,

√x - 1/√x = (√2 + 1) - (√2 - 1) = 2 (answer).