设P(x,y)为函数y=x-1(x>√3)图像上一动点,记m=(3x+y-5)/(x-1)+(x+3y-7)/(y-2),则当m最_数学解答

设P(x,y)为函数y=x-1(x>√3)图像上一动点,记m=(3x+y-5)/(x-1)+(x+3y-7)/(y-2),则当m最小时,点P的坐标是

人气：284 ℃　时间：2020-08-09 20:46:42

解答

答：y=x^2-1m=(3x+y-5)/(x-1)+(x+3y-7)/(y-2)=(3x+x^2-1-5)/(x-1)+(x+3x^2-3-7)/(x^2-1-2)=(x^2+3x-6)/(x-1)+(3x^2+x-10)/(x^2-3)m'(x)=(2x+3)/(x-1)-(x^2+3x-6)/(x-1)^2+(6x+1)/(x^2-3)-(6x^3+2x^2-20x)/(x^2-3)^2=...