4(a-b)(b-c)-(a-c)平方=0,试说明a+c=2b,

题目

4(a-b)(b-c)-(a-c)平方=0,试说明a+c=2b,

答案

4(a-b)(b-c)-(a-c)平方=0
4(a-b)(b-c)=(a-c)平方
4ab-4b^2-4ac-4bc=a^2-2ac+c^2
a^2+c^2+(2b)^2+2ac-4ab+4bc=0
(a+c-2b)^2=0
a+c-2b=0
a+c=2b