Question

if x+y+z=0 show that x^3+y^3+z^3=3xyz

Answer 1

HEY !!! HERE IS YOUR ANSWER 》》

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Answer 2

Given that x+y+z=0

We know that a³ + b³ + c³ - 3abc= (a + b +c)(a² + b² + c² - ab- bc - ac)

So, 

x³ + y³ + z³ - 3xyz= (x + y+ z)(x² + y² + z² - xy - yz - xz)
⇒ x³ + y³ + z³ - 3xyz = 0 * (x² + y² + z² - xy - yz - xz)
⇒x³ + y³ + z³ - 3xyz = 0
⇒ x³ + y³ + z³ = 3xyz

Hence Proved.