Question

If a+b+c=9 and a^2+b^2+c^2-3.Find the value of (1) ab+bc+ca and(2) a^3+b^3+c^3-3abc.​

Answer 1

Ans:- Given:- a+b+c=9, a^2+b^2+c^2 = 3

to find, ab+bc+ca and a^3+b^3+c^3-3abc

Now,

=> (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca

=> (9)^2 = 3 + 2(ab+bc+ca)

=> 81 -3 = 2(ab+bc+ca)

=> 78 = 2(ab+bc+ca)

=> ab+bc+ca = 39

a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-(ab+bc+ca)

=> (9) (3 - 39)

=> 9 × 36

=> 324

here is your answer

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