x>3,不等式(x^2-3x+1)/(x-3)>=m恒成立,求m的范围

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x>3,不等式(x^2-3x+1)/(x-3)>=m恒成立,求m的范围
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x>3,不等式(x^2-3x+1)/(x-3)>=m恒成立,求m的范围
x>3,不等式(x^2-3x+1)/(x-3)>=m恒成立,求m的范围

x>3,不等式(x^2-3x+1)/(x-3)>=m恒成立,求m的范围
(x²-3x+1)/(x-3)
=x(x-3)/(x-3)+1/(x-3)
=x+1/(x-3)
=(x-3)+1/(x-3)+3
x>3.x-3>0
所以(x-3)+1/(x-3)+3≥2√[(x-3)*1/(x-3)]+3=2+3=5
所以左边最小是5
所以m≤5