Question

If x+y+z=12
x^2+y^2+z^2=90
x^3+y^3+z^3-3xy=?​

Answer 1

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

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

12 =90 + 2( ab+bc+ca)

27 = ab +bc+ca

12*(90-27)

= 12*63 =756...right answer.