Question

if a+b+c=5 and ab+bc+ac=10, then find a^3+b^3+c^3-3abc= -25

Answer 1

(a+b+c)^2 =a^2+b^2+c^2+2(ab+bc+ca)
(5)^2=a^2+b^2+c^2+2*10
25-20=5=a^2+b^2+c^2

a^3+b^3+c^3-3abc
=(a+b+c) (a^2+b^2+c^2-(ab+bc+ca))
=5(5-10)
=5*-5= -25
Hence proved.

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