Question

If x= 1-√2, find the value of (x-1/x )^2 ?​

Answer 1

EXPLANATION.

⇒ x = 1 - √2.

As we know that,

We can write equation as,

⇒ 1/x = 1/1 - √2.

Rationalize the equation, we get.

⇒ 1/x = 1/1 - √2 x (1 + √2)/(1 + √2).

⇒ 1/x = (1 + √2)/(1 - 2).

⇒ 1/x = (1 + √2)/- 1.

⇒ 1/x = -(1 + √2).

To find :

⇒ (x - 1/x)².

Put the value in the equation, we get.

⇒ [(1 - √2) - (-)(1 + √2)]².

⇒ [(1 - √2) + (1 + √2)]².

⇒ [1 - √2 + 1 + √2]².

⇒ [2]² = 4.

⇒ (x - 1/x)² = 4.