Trying to find the right answer to this..

We know that x 3 + y 3 + z 3 - 3xyz = (x + y + z)(x 2 + y 2 + z 2 - xy - yz - zx) | Using Identity VIII = (0)(x 2 + y 2 + z 2 - xy - yz - zx) | ∵ x + y + z = 0 = 0 ⇒ x 3 + y 3 + z 3 = 3xyz.

Coordinate Geometry

Question

Wired Faculty App

If x + y + z = 0, show that x³ + y³ + Z³ = 3xyz.

Answer

We know that
x³ + y³ + z³ - 3xyz
= (x + y + z)(x² + y² + z²- xy - yz - zx)
| Using Identity VIII
= (0)(x² + y² + z² - xy - yz - zx)
| ∵ x + y + z = 0
= 0
⇒ x³ + y³ + z³ = 3xyz.