Question

if a+b+c=0, show that a^3+b^3+c^3=3abc. also find the value of -12^3+27^3+-15^3.

Answer 1

Given :-

=> a + b + c = 0
____________

We know that :-

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

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

=> a³+b³+c³-3abc = 0

=> a³+b³+c³ = 3abc
________________[PROVED]

____________________________________

2nd Part of the question :-

=> -12³+27³+(-15)³

=> -1728 + 19683 - 3375

=> 19683 - 5103

=> 14500
__________[ANSWER]

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