Rational equation my question
İf $ x+\frac{1}{x^2}=3$
 then find      $( x^2 -\frac{1}{x})^2 $ .
I tried factoring, taking squares of both sides and some other things that did not work.  what should i do? 

Contrary to $x+\frac{1}{x^2}=3$, the expresion $x-\frac{1}{x^2}$ cannot be constant because if $(x-\frac{1}{x^2})^2=a^2$ then one would have
$$x^3-3x^2+1=0\\x^3\mp ax^2-1=0$$ from which $$x=\pm\sqrt{\frac{2}{3\mp a}}$$ and this is not compatible with the three distinct possible (real) values of $x$.
An easy calculation gives $$\left(x-\frac{1}{x^2}\right)^2=\left(3-\frac{2}{x^2}\right)^2$$
