Get Answers to all your Questions

header-bg qa

If a+b+c=0 , then a^{3}+b^{3}+c^{3}  is equal to

(A) 0                           (B) abc                        (C) 3abc                      (D)      2abc

Answers (1)

(C) 3abc

Solution

We know that

a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)

Given, a+b+c=0     …..(1)

a^{3}+b^{3}+c^{3}=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc               …..(2)

Using equation 1 in equation 2 we have

\\a^{3}+b^{3}+c^{3}=(0)(a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc\\ a^{3}+b^{3}+c^{3}=3abc

Therefore option (C) is correct.           

 

Posted by

infoexpert24

View full answer