MCQ
Write the correct answer in the following: If $a + b + c = 0,$ then $a^3 + b^3 + c^3$ is equal to.
- A$0$
- B$abc$
- ✓$3abc$
- D$2abc$
✓
Answer
Correct option: C.
$3abc$
Now, $a^3 + b^3 + c^3 = (a + b + c)(a^2 + b^2 + c^2 - ab - be - ca) + 3abc$
$[$Using identity,$ a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - be - ca)] = 0 + 3abc$
$\therefore a + b + c = 0,$ given
$a^3 + b^3 + c^3 = 3abc$
$[$Using identity,$ a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - be - ca)] = 0 + 3abc$
$\therefore a + b + c = 0,$ given
$a^3 + b^3 + c^3 = 3abc$
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