Question

If x + y + z = 0 show that x3 + y3 + z3 = 3xyz

Answer 1

Answer:

We have

X3+y3+z3-3xyz=(X+y+z)(X2+y2+z2-xy-yz-zx)

now if X+y+z=0,then then the whole term Will become 0

so,X3+y3+z3=3xyz

Hence proved

Answer 2

Step-by-step explanation:

we know that

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

putx+y+z/0

x^3+y^3+z^3-3xyz=0/(x^2+y^2+z^2-xy-yz-zx)

x^3+y^3+z^3-3xyz=0

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