等比数列a+log(2)3,a+log(4)3,a+log(8)3
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等比数列a+log(2)3,a+log(4)3,a+log(8)3
求公比q.
求公比q.
[a+log(4)3]^2=[a+log(2)3][a+log(8)3]
[a+lg3/2lg2]^2=[a+lg3/lg2][a+lg3/3lg2]
令x=lg3/(6lg2)
则(a+3x)^2=(a+6x)(a+2x)
a^2+6ax+9x^2=a^2+8ax+12x^2
-3x^2=2ax
显然x不等于0
所以a=-3x/2
所以q=(a+3x)/(a+6x)=(-3x/2+3x)/(-3x/2+6x)=1/3
[a+lg3/2lg2]^2=[a+lg3/lg2][a+lg3/3lg2]
令x=lg3/(6lg2)
则(a+3x)^2=(a+6x)(a+2x)
a^2+6ax+9x^2=a^2+8ax+12x^2
-3x^2=2ax
显然x不等于0
所以a=-3x/2
所以q=(a+3x)/(a+6x)=(-3x/2+3x)/(-3x/2+6x)=1/3
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