已知:a^2 b^2 c^2 2ab 2bc 2ca=0,化简代数式1/2a^3-1/2ab^2-1/2ac^2.

已知:a^2 b^2 c^2 2ab 2bc 2ca=0,化简代数式1/2a^3-1/2ab^2-1/2ac^2.
已知:a^2 b^2 c^2 2ab 2bc 2ca=0,化简代数式1/2a^3-1/2ab^2-1/2ac^2.

已知:a^2 b^2 c^2 2ab 2bc 2ca=0,化简代数式1/2a^3-1/2ab^2-1/2ac^2.
a平方+b平方+c平方+2ab+2bc+2ca=0
(a+b+c)^2=0
a+b+c=0
a=-(b+c)
1/2a^3-1/2ab^2-1/2ac^2=a/2(a^2-b^2-c^2)
=a/2[(b+c)^2-(b^2+c^2)]
=a/2(2bc)
=abc