Question

find the value of x²+1/x², if x-1/x=√3​

Answer 1

Given:-

• Value of x-1/x =√3

To find:-

• Value of x^2 + 1/x^2

Then,

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

Now put the value of x-1/x in above formula

$\tt \implies( { \sqrt{3} })^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \tt \implies 3 = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \tt \implies {x}^{2} + \frac{1}{ {x}^{2} } = 3 + 2 = \red5$