I should find $A,B$ and $C$. I know answers but can't figure out how to solve it. Anyone?
We are to find value of $x^4+y^4+z^4$ when $x, y$ and $z$ are real numbers which satisfy the following three equalities: $$x+y+z=3$$ $$x^2+y^2+z^2=9$$ $$xyz=-2$$
Firstly, it follows from the first two equalities that $$xy+yz+zx=A$$
Next, using $$(x^2+y^2+z^2)^2=x^4+y^4+z^4+B[(xy)^2+(yz)^2+(zx)^2],$$ we have $x^4+y^4+z^4=C$.