Question

If $x^2+\frac{1}{x^2}=3$, find the value of $x+\frac{1}{x}$.

Answer 1

$x^2+\frac{1}{x^2}=3$

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

$\Rightarrow {(x+\frac{1}{x})}^2=3+2=5$

$\Rightarrow x+\frac{1}{x}=\pm \sqrt{5}$

$\therefore x+\frac{1}{x}=\pm \sqrt{5}$