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  • a+b+c=5 and ab+bc+ca=10. Show that a^3 +b^3 +c^3 -3abc= -25

a+b+c=5 and ab+bc+ca=10. Show that a^3 +b^3 +c^3 -3abc= -25

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

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

(a+b+c)²=(a²+b²+c²) +2(ab+bc+ac)
    OR,  5²    =(a²+b²+c²)+ 2(10)
   Or,  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

 

Posted by

shubham.krishnan

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