Question

若实数abc满足a^2+b^2不等于0,a^3+(a^2)c-abc+(b^2)c+b^3=0,则a+b+c的值是什么

Answer 1

a^3+(a^2)c-abc+(b^2)c+b^3

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

=(a+b)(a^2-ab+b^2)+c(a^2-ab+b^2)

=(a+b+c)(a^2-ab+b^2)

=0

a^2-ab+b^2=(a-b/2)^2+3b^2/4≥0

当且仅当a=0,b=0时取等,这与题意不符.

故a+b+c=0