System of 2 non-linear equations

Question

I have this system:

$$uv= -\dfrac{p}{3}$$

$$u^3+v^3=-q$$

I have to find $u$ and $v$.

I've read somewhere that this system can be transformed in a quadratic equation and then easily solved.

If this is the right method, how can i do that?

Or if not, how do i solve it?

Answer 1

Since $u^3v^3 = -\dfrac{p^3}{27}$, and setting $ x = u^3$ and $y = v^3$, we have the system

$$xy = -\dfrac{p^3}{27}$$

$$x +y = - q $$

I think you can continue from here.