Question

若a+b=-1,则a^3+b^3-3ab的值为

Answer 1

正确答案：1

a^3+b^3+3ab

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

=1x(a^2-ab+b^2)+3ab

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

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

因为a+b=1

所以,原式=(a^2-ab+b^2)+3ab

=a^2+2ab+b^2

=(a+b)^2

=1