Question

设A={x|x^2-4x+3<=0}，B={x|x^2-(a+1)x+a<0}，B包含于A，求实数a

的范围，谢谢！
a的范围，不好意思手机看不清图片的！

Answer 1

Answer 2

A={x|x^2-4x+3≤0}
={x|(x-3)(x-1)≤0}
={x|1≤x≤3}
B={x|x^2-(a+1)x+a<0}
={x| (x-a)(x-1)<0
case 1: a>1
B= {x| 1<x<a }
B is subset of A
=>a≤3
solution for case 1: 1<a≤3

case 2: a=1
B={ x| (x-1)^2 <0 } = Φ is subset of A

case 3: a< 1
B= {x| a<x<1 }
B is subset of A
=> a≥1
no solution for case 3:

B is subset of A
=> case 1 or case 2 or case 3
=> 1≤a≤3

Answer 3

追答

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