已知x>1 求(x^2-x+3)/(x-1)最小值(用均值不等式求)谢谢
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![已知x>1 求(x^2-x+3)/(x-1)最小值(用均值不等式求)谢谢](/uploads/image/z/7622969-41-9.jpg?t=%E5%B7%B2%E7%9F%A5x%3E1+%E6%B1%82%28x%5E2-x%2B3%29%2F%28x-1%29%E6%9C%80%E5%B0%8F%E5%80%BC%EF%BC%88%E7%94%A8%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F%E6%B1%82%EF%BC%89%E8%B0%A2%E8%B0%A2)
已知x>1 求(x^2-x+3)/(x-1)最小值(用均值不等式求)谢谢
已知x>1 求(x^2-x+3)/(x-1)最小值(用均值不等式求)谢谢
已知x>1 求(x^2-x+3)/(x-1)最小值(用均值不等式求)谢谢
x>1则x-1>0
原式=(x²-x)/(x-1)+3/(x-1)
=x(x-1)/(x-1)+3/(x-1)
=x+3/(x-1)
=(x-1)+3/(x-1)+1≥2√[(x-1)*3/(x-1)]+1=2√3+1
所以最小值是2√3+1