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Question

If a+b+c=0, prove that identities 3(a2+b2+c2)(a5+b5+c5)=5(a3+b3+c3)(a4+b4+c4).

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Solution

a2+b2+c2=2q,a5+b5+c5=5qr
a3+b3+c3=3r,a4+b4+c4=2q2
LHS;-
3(a2+b2+c2)(a5+b5+c5)
=3(2q)(5qr)=30q2r
RHS;-
5(a3+b3+c3)(a4+b4+c4)
=5(3r)(2q2)=30q2r
Hence proved.

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