Question

if x^2+1/x^2=3,find the value of x-1/x.
using identities ​

Answer 1

Step-by-step explanation:

x^2 + 1/x^2 -2 = {x-1/x}^2

3 -2 = {x - 1/x}^2

x-1/x = 1

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 3 \\ \\ = > {(x - \frac{1}{x} )}^{2} + 2.x. \frac{1}{x} = 3 \\ \\ = > ( {x - \frac{1}{x}) }^{2} + 2 = 3 \\ \\ = > ( {x - \frac{1}{x}) }^{2} = 3 - 2 \\ \\ = > ( {x - \frac{1}{x}) }^{2} = 1 \\ \\ = > ( {x - \frac{1}{x}) }^{2} = ( {1)}^{2} \\ \\ = > x - \frac{1}{x} = 1.$

This is the required Answer.