Hello HavenBombelli's method is new to me! I should not have thought of using and .

I agree with your equations, although I think that in order to justify the last two you also need to cube both sides of (2) to get:

and then subtract this from your previous equation, before dividing by 2 to get:

Then it's a simple matter of eliminating by substitution:

Grandad

, since the discriminant of the second factor is negative