Question

If a+b+c=0 then prove that a^3+b^3+c^3=3abc
Only when a=b=c.

Answer 1

Answer:

a3 +b3 + c3 – 3abc = (a+b+c) (a2 + b2 + c2 – ab – bc – ca) If a+b+c = 0 , then your given statement is true Also if a=b=c then either all are positive numbers or all should be negative numbers which cannot sum upto zero.

Step-by-step explanation:

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Answer 2

Given:

a+b+c = 0

a+b = -c

cubing both sides,

(a+b)³ = (-c)³

a³ + b³ + 3ab(a+b) = -c³

a³ + b³ - 3abc = -c³

a³ + b³ + c³ = 3abc