Question:
If $x-1 / x=-1$, find the value of $x^{2}+1 / x^{2}$
Solution:
We have, $x-1 / x=-1$
Now, $(x-1 / x)^{2}=x^{2}+(1 / x)^{2}-2 * x * 1 / x$
$\Rightarrow(x-1 / x)^{2}=x^{2}+1 / x^{2}-2$
$\Rightarrow(-1)^{2}=x^{2}+1 / x^{2}-2[\therefore x-1 / x=-1]$
$\Rightarrow 2+1=x^{2}+1 / x^{2}$
$\Rightarrow x^{2}+1 / x^{2}=3$