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Question

If a+b+c=0 then (a2bc+b2ca+c2ab)=?
(a) 1 (b) 0 (c) -1 (d) 3

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Solution

a+b+c=0a3+b3+c3=3abc

Thus, we have:

a2bc+b2ca+c2ab=a2×abc×a+b2×bca×b+c2×cab×c=a3abc+b3abc+c3abc=a3+b3+c3abc=3abcabc=3​​​​​​​

(d) 3


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