Question

4 — Ifx+y+z= 0 , show that x+y+z= 3 Хуz​

Answer 1

Answer:

We know that

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

Putting x + y + z = 0,

x³ + y³ + z³ - 3xyz = (0) ( x² + y² + z² - xy - yz - zx)

x³ + y³ + z³ - 3xyz = 0

x³ + y³ + z³ = 3xyz