Question

x-y+z=5 and x^2+y^2+z^2=49 find the value of zx-xy-yz

Answer 1

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

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

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

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

               =  5 ^2 - 49 / 2

               = 25 - 49/2

               = -24 /2 = -12