求函数y=x^2-3x+6/x-2(x>2)的取值范围

/>y=(x^2-3x+6)/(x-2) (x>2)y=(x²-4x+x-2+8)/(x-2) y=[(x-2)²+(x-2)+8]/(x-2) 令x-2=t,则t>0y=[(x-2)²+(x-2)+8]/(x-2) =(t²+t+8)/t=t+1+8/t=t+8/t+1 (t>0)≥2√(t*8/t)+1=4√2+1当且仅当t=8/t即t=2√2,x=2+2√2时等号成立所以y=x^2-3x+6/x-2(x>2)的取值范围是：y≥4√2+1