(t^2+t+1/4)/(4t-6)的最小值如何求?

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(t^2+t+1/4)/(4t-6)的最小值如何求?
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(t^2+t+1/4)/(4t-6)的最小值如何求?
(t^2+t+1/4)/(4t-6)的最小值如何求?

(t^2+t+1/4)/(4t-6)的最小值如何求?
(t^2+t+1/4)/(4t-6)=[(t-3/2)^2+4t-2]/4(t-3/2)
=(t-3/2)/4+(4t-2)/4(t-3/2)
=(t-3/2)/4+[4(t-3/2)+4]/4(t-3/2)
=(t-3/2)/4+1/(t-3/2)+1
≥2√[(t-3/2)/4·1/(t-3/2)]+1
=2
当(t-3/2)/4=1/(t-3/2),即t=7/2或-1/2时取得等号

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