Question

If $x^2+\frac{1}{x^2}=51,$ find $x-\frac{1}{x}$

Answer 1

solution :-

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

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

$=51-2$

$=49$

$\Rightarrow x-\frac{1}{x}=\pm 7$