Question

If $x^2+\frac{1}{x^2}=51$, find the value of $(x-\frac{1}{x})$

Answer 1

Given,

$x^2+\frac{1}{x^2}=51$

or, ${(x-\frac{1}{x})}^2+2.x.\frac{1}{x}=51$

or, ${(x-\frac{1}{x})}^2=51-2$

or, ${(x-\frac{1}{x})}^2=49$

or, $(x-\frac{1}{x})=\pm 7.$