Question

If x^3+y^3+z^3=3xyz and x+y+z=0 then the value of(x+y)^2/xy +(y+z)^2 /yz +(z+x)^2 /zx is

Answer 1

x^3+y^3+z^3-3xyz=x+y+z(x^2+y^2+z^2-2xy-2yz-2xz

" = "

x^3+y^3+z^3=3xyz

x^3/xyz+y^3/xyz+z^3/xyz=3

x^2/yz+y^2/xz+z^2/xy=3

x+y+z=0

x=-(y+z),y=-(x+z),z=-(x+y)---------(1)

(y+z)^2/yz+(x+z)^2/xz+(x+y)^2=3

It is the answer. Hope u understood.