求函数y=(x²-3x+3)/(x-2) (x>2)的最小值，请不要跳步，谢谢
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求函数y=(x²-3x+3)/(x-2)
(x>2)的最小值
y=(x²-3x+3)/(x-2)
=[x(x-2)-x+3]/(x-2)
=[x(x-2)-(x-2)+1]/(x-2)
=x(x-2)/(x-2)-(x-2)/(x-2)+1/(x-2)
=(x-1)+1/(x-2)
=(x-2)+1/(x-2)+1
因为x＞2,
x-2＞0
所以式中的(x-2)+1/(x-2)≥2,
即
y=(x-2)+1/(x-2)+1有最小值
2+1=3
(x>2)的最小值
y=(x²-3x+3)/(x-2)
=[x(x-2)-x+3]/(x-2)
=[x(x-2)-(x-2)+1]/(x-2)
=x(x-2)/(x-2)-(x-2)/(x-2)+1/(x-2)
=(x-1)+1/(x-2)
=(x-2)+1/(x-2)+1
因为x＞2,
x-2＞0
所以式中的(x-2)+1/(x-2)≥2,
即
y=(x-2)+1/(x-2)+1有最小值
2+1=3
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