If x + y + z = 0 then x3 +...

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If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

A. 0

B. 6xyz

C. 12xyz

D. xyz

Answer: Option B

Solution(By Examveda Team)

As we know
a³ + b³ + c³ + 3abc = (a² + b² + c² - ab - bc - ca)(a + b + c)
When, a + b + c = 0
Then a³ + b³ + c³ - 3abc = 0
When, x + y + z = 0
⇒ x³ + y³ + z³ = 3xyz
⇒ x³ + y³ + z³ + 3xyz = 3xyz + 3xyz
⇒ x³ + y³ + z³ + 3xyz = 6xyz

This Question Belongs to Arithmetic Ability >> Simplification

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