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a+b+c=5
ab+bc+ca=10
show that a cube +b cube +c cube -3abc= -25
pls show me how to do it ,its for tmmr.

Answer :

Adithya1234
Given a+b+c=5 and ab+bc+ac=10

a³+b³+c³-3abc=(a+b+c) (a²+b²+c²-(ab+bc+ca))

(a+b+c)²=(a²+b²+c²) +2(ab+bc+ac)
     5²    =(a²+b²+c²)+ 2(10)
    25    =(a²+b²+c²)+20
(a²+b²+c²)=25-20=5

a³+b³+c³-3abc=(a+b+c) (a²+b²+c²-(ab+bc+ca))
                    =5×(5-10)
                    =5×-5
a³+b³+c³-3abc=-25

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