已知a=m/2+1,b= m/2+2,c= m/2+3,求a^2+2ab+b^2-2ac-abc+c^2的值
问题描述：
已知a=m/2+1,b= m/2+2,c= m/2+3,求a^2+2ab+b^2-2ac-abc+c^2的值
答
a^2+2ab+b^2-2ac-abc+c^2
=(a+b)^2-2c(a+b)+c^2+2bc-abc
=(a+b-c)^2+bc(2-a)
=(m/2+1+m/2+2-m/2-3)^2+(m/2+2)(m/2+3)(2-m/2-1)
=m^2/4+(m^2/4+5m/2+6)(1-m/2)
=m^2/4+m^2/4+5m/2+6-m^3/8-5m^2/4-3m
=-m^3/8-3m^2/4-m/2+6
答
a^2+2ab+b^2-2ac-abc+c^2 =(a+b)^2-2c(a+b)+c^2+2bc-abc =(a+b-c)^2+bc(2-a) =(m/2+1+m/2+2-m/2-3)^2+(m/2+2)(m/2+3)(2-m/2-1) =m^2/4+(m^2/4+5m/2+6)(1-m/2) =（m^2）/4+（m^2）/4+5m/2+6-（m^3）/8-）（5m^2）/4-3...