Question

$$x+y=1, \,  x^2+y^2=2$$ ise $$ x^3+y^3=?$$

Answer 1

1) $xy=\frac{1}{2}((x+y)^2-(x^2+y^2))=-\frac12$.
2) $x^3+y^3=(x+y)(x^2+y^2-xy)=\frac52$.