Question

If x + y + z=0 and x
^2 + y^2 + z^2=12, find the value

of xy + yz + zx​

Answer 1

Answer:

(x+y+z)²=x²+y²+z²+2(xy+yz+zx)

0=12+2(xy+yz+zx)

2(xy+yz+zx)=-12

xy+yz+zx=-6

Answer 2

x + y + z = 0

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

(0)² = 12 + 2(xy + yz + zx)

0 = 12 + 2(xy + yz + zx)

2(xy + yz + zx) = -12

xy + yz + zx = -12/2

xy + yz + zx = -6