$a^{3} + b^{3} + c^{3} = 3 a b c$ , if:

a + b + c = 3

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a = b = c

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a + b + c = 0

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a b c = 0

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Solution

The correct option is C $a + b + c = 0$
We know,
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b c - c a)$ .

Here, clearly $a^{3} + b^{3} + c^{3} = 3 a b c$ only if $a + b + c = 0$ .

$∴ a^{3} + b^{3} + c^{3} = 3 a b c$ , if $a + b + c = 0$ .

Hence, option $B$ is correct.

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Similar questions

If a+b+c=0 then $(a^{3} + b^{3} + c^{3})$ is
(a) 0 (b) abc (c) 2abc (d) 3abc

a + b + c = 0

a^{3} + b^{3} + c^{3} = 3 a b c

a^{3} + b^{3} + c^{3} - 3 a b c

a + b + c = 0

Evaluate $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{(a + b + c)}, where (a + b + c) \neq 0$ .

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