Question

if x+y+z=0 prove x^2/yz+y^2/zx+z^2/xy=3

Answer 1

Step-by-step explanation:

x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx)

x3+y3+z3-3xyz=0

x3+y3+z3=3xyz

(x3+y3+z3)/xyz=3

(x3/xyz)+(y3/xyz)+(z3/xyz)=3

x2/xy+y2/zx+z2/xy=3