Question

if a + 2 b + 3 C is equal to zero prove that a^ 3 + 8b^3 + 27c^3 equal to 18 ABC

Answer 1

we know,
a + b + c = 0
then
a³ + b³ + c³ = 3abc
use this here
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a + (2b) +(3c) =0

so , a³ +(2b)³ + (3c)³ = 3a(2b)(3c) = 18abc

a³ +8b³ +27c³ = 18abc