Question

If x+y+z=0 then how can you prove that x³+y³+z³=3xyz?

Answer 1

★ GIVEN :

x + y + z = 0 ——(1)

★ TO PROVE :

x³ + y³ + z³ = 3xyz

★ PROOF :

x + y + z = 0 ——(1)

→ x + y = - z ——(2)

Cubing both sides. We get,

(x + y)³ = (- z)³

→ x³ + y³ + 3xy(x + y) = -z³

→ x³ + y³ + 3xy(-z) = -z³ [From Equation 2]

→ x³ + y³ - 3xyz = -z³

→ x³ + y³ + z³ = 3xyz

Hence Proved !

Answer 2

Answer:

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