Question

求解一道数学题，写出详细步骤 已知abc≠0,且a+b+c=0,则代数式a^2/bc+b^2/ac+c^2/ab的值为多少?

Answer 1

a+b+c=0,a+b=-c

a^2/bc+b^2/ac+c^2/ab
通分
=(a^3+b^3+c^3)/abc
=[(a+b)(a^2-ab+b^2)+c^3]/abc
=[-c(a^2-ab+b^2)+c^3]/abc
={-c[(a+b)^2-3ab]+c^3}/abc
=[-c(c^2-3ab)+c^3]/abc
=(-c^2+3abc+c^3)/abc
=3abc/abc
=3

追问

由a^3+b^3到(a+b)(a^2-ab+b^2)怎么变的

追答

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