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"If a+b+c = 0

Then a³+b³+c³ = 3abc"

Now what if a+b+c is not equal to 0 , then how do you solve a³+b+³+c³ ?

Solve this-

12³ +14³+2³.

$W e k n o w t h e i d e n t i t y, a^{3} + b^{3} + c^{3} = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a) + 3 a b c ..... (1) N o w, i f a + b + c = 0 T h e n, e q u a t i o n (1) b e c o m e s, a^{3} + b^{3} + c^{3} = 0 \times (a^{2} + b^{2} + c^{2} - a b - b c - c a) + 3 a b c \Rightarrow a^{3} + b^{3} + c^{3} = 0 + 3 a b c \Rightarrow a^{3} + b^{3} + c^{3} = 3 a b c N o w, u \sin g t h e i d e n t i t y, 12^{3} + 14^{3} + 2^{3} = (12 + 14 + 2) (12^{2} + 14^{2} + 2^{2} - 12 \times 14 - 14 \times 2 - 2 \times 12) + 3 \times 12 \times 14 \times 2 = (28) (144 + 196 + 4 - 168 - 28 - 24) + 1008 = 28 \times 124 + 1008 = 3472 + 1008 = 4480 H e n c e, 12^{3} + 14^{3} + 2^{3} = 4480$

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