Question

等差数列的求证 已知a,b,c三个实数满足(c-a)^2 -4（a-b）(b-c)=0,求证a,b,c成等差数列.我知道

Answer 1

证明：

(c-a)^2-4(a-b)(b-c)=0

(a-c)^2-4(a-b)(b-c)=0

(a-b+b-c)^2-4(a-b)(b-c)=0

(a-b)^2+(b-c)^2+2(a-b)(b-c)-4(a-b)(b-c)=0

(a-b)^2+(b-c)^2-2(a-b)(b-c)=0

[(a-b)-(b-c)]^2=0

(a-2b+c)^2=0

a-2b+c=0

a+c=2b

b-c=a-b

a,b,c成等差数列.