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

-20

If x + y + z = 0

$x^2 + y^2+ z^2 =40$

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put z = 0

If x + y = 0

$x^2 + y^2 =40$

xy + yz + zx = xy = ? ( Because z = 0)

( x + y )² = x² + y² + 2xy

(0 )² = 40 + 2xy

2xy = -40

xy = -20