Given$ X+Y=3 $,$ xy= -10$, find value of $x^2 + y^2$

Question

Find value of $x^2 + y^2$ given that $x+y= -3$ and $xy= -10$

Answer 1

Hint:

$x+y=-3$ $$\implies (x+y)^2=9$$ $$\implies x^2+y^2+2xy =9$$ Can you continue?

Answer 2

after squaring we get $$x^2+y^2+2xy=9$$ with $$xy=-10$$ we obtain $$x^2+y^2-20=9$$ can you proceed?

Answer 3

$x^2+y^2=(x+y)^2-2xy=(-3)^2-2 \cdot (-10)=...$