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  • If a + b + c = 12, then a² + b² + c² = 90, then find the value of a³ + b³ + c³ - 3abc

If a + b + c = 12, then a² + b² + c² = 90, then find the value of a³ + b³ + c³ - 3abc

Answers (1)

a+b+c = 12

a2+b2+c2 = 90

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

(a+b+c)2= a2+b2+c2-2(ab+bc+ca)

122 = 90 -2(ab+bc+ca)

(ab+bc+ca) = (144-90)/2 = 27

Now 

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

                         = 12 x (90- 27)

                        = 12 x 63

                       = 756

Posted by

Ravindra Pindel

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