Question

If a+b+c=3 and a^2+b^2+c^2=13 and a^3+b^3+c^3=27 then find the value of abc.

Answer 1

Answer:

(a+b+c)2= a2+b2+c2+2 (ab+bc+ca)

Or,9=13+2 (ab+bc+ca)

Or,(ab+ba+ca)=-2

Next,

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

27-3abc=(13+2)*9

27-3abc=135

3abc=27-135

abc=-36