Question

if X + Y + Z is equal to zero show that x cube + y cube + Z cube is equal to 3 x yz

Answer 1

hey mate,,here is ur ans..

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

But, x+y+z = 0

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

⇒x³ + y³ + z³ - 3xyz= 0

⇒x³ + y³ + z³ = 3xyz

#hope it helps.