Question

if a+b+C = 9 and ab+bc+ca = 26 , then the value of a^3+b^3+c^3 -3 ABC is

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Answer 1

Answer:

a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2- ab-bc-ca)= (a+b+c){a^2+b^2+c^2 - (ab+bc+ca)=(9) a^2 + b^2 + c^2 - (26) ____i

Now let's find the value of a^2+b^2+c^2

We know that, (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca)

=> (9)^2=a^2+b^2+c^2+2(26)

=> 81 = a^2+b^2+c^2+52

=>a^2+b^2+c^2 = 81-52

=>a^2+b^2+c^2= 29

Putting the value of a^2+b^2+c^2 we havein equation i we have ,

a^3+b^3+c^3 -3abc = (9)(29-26)= 9 × 3 = 27