Question : If $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers), then what is the value of $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}$?

Question : If $x^2-xy+y^2=2$ and $x^4+x^2y^2+y^4=6$, then the value of $(x^2+xy+y^2)$ is:

Question : If $x+y+z=0$ and $x^2+y^2+z^2=40$, then what is the value of $x y+y z+z x?$

Question : If $x=1-y$ and $x^2=2-y^2$, then what is the value of $xy$?

Question : $x,y,$ and $z$ are real numbers. If $x^3+y^3+z^3 = 13, x+y+z = 1$ and $xyz=1$, then what is the value of $xy+yz+zx$?