Question:
If $a+b+c=0$, then $a^{3}+b^{3}+c^{3}=?$
(a) 0
(b) $a b c$
(c) $2 a b c$
(d) $3 a b c$
Solution:
(d) 3abc
$a+b+c=0$
$\Rightarrow a+b=-c$
$\Rightarrow(a+b)^{3}=(-c)^{3}$
$\Rightarrow a^{3}+b^{3}+3 a b(a+b)=-c^{3}$
$\Rightarrow a^{3}+b^{3}+3 a b(-c)=-c^{3}$
$\Rightarrow a^{3}+b^{3}+c^{3}=3 a b c$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.