Question

Find the value of x2+1/x2if x-1/x=root 3

Answer 1

Here is your answer brother

(x - 1/x) = √3

Squaring both side

(x - 1/x)^2 = 3

x^2 + 1/x^2 - 2 = 3

x^2 + 1/x² = 3+2

x^2 +1/x^2 = 5

Hope it's helpful

Answer 2

Given:

The given value is

$x - \frac{1}{x} = \sqrt{3}$

To find:

We have to find the value of the below expression.

${x}^{2} + \frac{1}{ {x}^{2} }$

Solution:

The given expression is

${x}^{2} + \frac{1}{ {x}^{2} }$

It can be simplified as follows-

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

Putting the value of x-1/x we get-

${√3}^{2} + 2 \\ = 3 + 2 \\ = 5$

The value of the expression is 5.