Question

if ×+y+z=0show that ×3+y3+z3=3xyz​

Answer 1

Step-by-step explanation:

Given

x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) x3+y3+z3-3xyz=0×(x2+y2+z2-xy-yz-zx) x3+y3+z3-3xyz=0 x3+y3+Z3=3xyz

Answer 2

Answer:

Given x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3+y 3+3x 2 y+3xy 2 =−z 3

⟹x 3 +y 3+3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3+y 3−3xyz=−z 3

⟹x 3+y 3 +z 3=3xyz