求y=(x^2+8)/(x-1) (x>1)的最小值

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求y=(x^2+8)/(x-1)(x>1)的最小值求y=(x^2+8)/(x-1)(x>1)的最小值求y=(x^2+8)/(x-1)(x>1)的最小值因为x>1所以x-1>0所以y=(x^2+8)/(

求y=(x^2+8)/(x-1) (x>1)的最小值
求y=(x^2+8)/(x-1) (x>1)的最小值

求y=(x^2+8)/(x-1) (x>1)的最小值
因为x>1
所以x-1>0
所以y=(x^2+8)/(x-1)
=[(x-1)^2+2(x-1)+9]/(x-1)
=(x-1)+9/(x-1)+2
≥2√[(x-1)*9/(x-1)]+2
=2*3+2
=8

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