中科新闻网微单 单反:初一数学
来源：百度文库 编辑：中科新闻网 时间：2024/05/05 23:54:30
a^2+b^2+c^2+2ab+2bc+2ca=0
化简1/2a^3-1/2ab^2-1/2ac^2
化简1/2a^3-1/2ab^2-1/2ac^2
a^2+b^2+c^2+2ab+2bc+2ca=0
(a+b+c)^2=0
a+b+c=0
1/2a^3-1/2ab^2-1/2ac^2
=1/2a(a^2-b^2)-1/2ac^2
=1/2a(a+b)(a-b)-1/2ac^2
=-1/2ac(a-b)-1/2ac^2
=-1/2ac(a-b+c)
=-1/2ac(-2b)
=abc
a^2+b^2+c^2+2ab+2bc+2ca
=a^2+b^2+c^2+ab+bc+ca+ab+bc+ca
=(a^2+ab+ca)+(b^2+bc+ab)+(c^2+bc+ca)
=a(a+b+c)+b(a+b+c)+c(a+b+c)
=(a+b+c)^2=0
所以：a+b+c=0，b=a+c
1/2a^3-1/2ab^2-1/2ac^2
=1/2a(a^2-b^2)-1/2ac^2
=1/2a(a+b)(a-b)-1/2ac^2
=-1/2ac(a-b)-1/2ac^2
=-1/2ac(a-b+c)
=-1/2ac(-2b)
=abc