Question

If x =1+ root 2 .Then find value of (x-1/x)

Answer 1

ANSWER:-

Given:

x = 1+ √2.

To find:

Find the value of (x-1/x).

Solution:

Given

x = 1+ √2

So,

$\frac{1}{x} = \frac{1}{1 + \sqrt{2} }$

Rationalizing the denominator we get;

$= > \frac{1}{1 + \sqrt{2} } \times \frac{1 - \sqrt{2} }{ 1 - \sqrt{2} } \\ \\ = > \frac{1 - \sqrt{2} }{(1) {}^{2} - ( { \sqrt{2} )}^{2} } \\ \\ = > \frac{1 - \sqrt{2} }{1 - 2} \\ \\ = > \frac{1 - \sqrt{2} }{ - 1} = \sqrt{2} - 1$

Now,

x- 1/x = 1+ √2 - √2 -1

x -1/x = 0

Hope it helps ☺️