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  • If a+b+c=0 , then a^{3}+b^{3}+c^{3} is equal to (A) 0 (B) abc (C) 3abc (D) 2abc

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

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