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Question

If a+b+c=4 and ab+bc+ca=6., find the value of a3+b3+c33abc

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Solution

According to the problem:
Let the use a3+b3+c3+3abc=(a+b+c)(a2+b2+c2abbcca)
=4(a2+b2+c2)4(ab+bc+ca)
=4(a+b+c)(a+b+c)6
=4×4×44×6
=6424
=40

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