If x + y + z = 0 and $x^2 + y^2+ z^2 =40$, then what is the value of xy + yz + zx?
Answer & explanation
Correct answer: option 1
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