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Question

$$a^3+b^3+c^3=3abc$$, if:


A
a+b+c=3
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B
a=b=c
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C
a+b+c=0
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D
abc=0
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Solution

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

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

$$\therefore a^3 + b^3 + c^3=3abc$$, if $$a + b + c =0$$.

Hence, option $$B$$ is correct.

Mathematics

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