若x>1,求y=2x+x+1/x-1最小值
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y=2x+(x+1)/(x-1)
=2x+(x-1+2)/(x-1)
=2x+1 +2/(x-1)
=2(x-1) +2/(x-1) +3
=2[(x-1)+1/(x-1)] +3
x>1 x-1>0，由均值不等式得(x-1)+ 1/(x-1)≥2
2[(x-1)+1/(x-1)] +3≥7
y≥7，ymin=7
=2x+(x-1+2)/(x-1)
=2x+1 +2/(x-1)
=2(x-1) +2/(x-1) +3
=2[(x-1)+1/(x-1)] +3
x>1 x-1>0，由均值不等式得(x-1)+ 1/(x-1)≥2
2[(x-1)+1/(x-1)] +3≥7
y≥7，ymin=7
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