Question

if. a+b+c=0. show. that. A³+b³+c³=3abc
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Answer 1

Answer:

a3 + b3 + c3 - 3abc = (a+b+c)(a2 + b2 + c2 - ab - bc - ca)

When a+ b+ c = 0,

a3 + b3 + c3 - 3abc = (0)(a2 + b2 + c2 - ab - bc - ca)

=​ a3 + b3 + c3 - 3abc = (0)

Hence,  

a3 + b3 + c3= 3abc

Step-by-step explanation:

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Answer 2

Given, a+b = - c

or, a³+b³+3ab(a+b) = - c³ (cubing both sides)

or, a³+b³+c³-3abc = 0

or, a³+b³+c³ = 3abc