Question

if a + 2 b + c =0; then show that a^3 + 8b^3 + c^3=6abc


Please solve it guys fast

Answer 1

Hey !!

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Here is your answer !!!
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since !!

a + 2b + c = 0 ( Given )
a + 2b = - c

on cubing both sides !!

( a + 2b )3 = ( - c )3

a3 + 8b3 + 3 a×2b (a +2b ) = - c3
a3 + 8b3 + 6ab (a + 2b ) = - c3

As we know a + 2b = - c

so

a3 + 8b3 + 6ab (- c) = - c3
a3 + 8b3 +c3 -6abc = 0
a3 + 8b3 + c3 = 6abc
Proved !!

Hope this helps you ^ _ ^ !!!

Answer 2

hello friend,

a + 2b + c = 0 ( Given )a + 2b = - con cubing both sides !!( a + 2b )3 = ( - c )3a3 + 8b3 + 3 a×2b (a +2b ) = - c3a3 + 8b3 + 6ab (a + 2b ) = - c3As we know a + 2b = - c soa3 + b3 + 6ab (- c) = - c3a3 + b3 +c3 -6abc = 0a3 + b3 + c3 = 6abc

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