Question

If x+y+z =0 then x×x÷yz+y×y÷zx+z×z÷xy is equal to options. A .3. B.27. C.1 D.-3

Answer 1

Answer: Option A : 3

Explaination :

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