Question

If a^2 +b^2+c^2=83 and a+b+c=15 then find the value of ab+bc+ca

Answer 1

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

(15)^2=83+2(ab+bc+ca)

225–83=2(ab+bc+ca)

142/2=71=ab+bc+ca

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

=(15)(83–71)

=15×12

=180 , Answer