a,b,c成等比 b^2=ac
1/a,1/b,1/c成等差 2/b=1/a+1/c=(a+c)/ac=(a+c)/b^2
2=(a+c)/b
2b=a+c
a,b,c即成等差也成等比
a=b=c 证明如下
b^2=ac
2b=a+c 4b^2=(a+c)^2=a^2+2ac+c^2=a^2+c^2+2b^2
2b^2=a^2+c^2
a^2-b^2=b^2-c^2
(a-b)(a+b)=(b-c)(b+c)
∵a-b=b-c
∴a+b=b+c
a=c
2b=a+c=2a
a=b
f(x)=ax^2+ax+a
=a(x+1/2)^2+3a/4
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