Question

x+y+z=0 then find x^2/yz+y^2/zx+z^2/xy

Answer 1

Step-by-step explanation:

x+y+z=0

x+y=−z(1)

Cubing both sides,

x3+y3+3xy(x+y)=−z3

From (1),

x3+y3+3xy(−z)=−z3

x3+y3+z3=3xyz

Now, dividing both sides by xyz ,

x3xyz+y3xyz+z3xyz=3

x2yz+y2xz+z2xy=3