Question

已知集合A={x/x^2-3x-10≤0},A是B的子集,B={x/m-6≤x≤2m-1},求实数m的取值范围

Answer 1

3<=m<=4
由A={x|x^2-3x-10≤0}
={x| (x-5)(x+2)≤0}
= { x| -2≤x≤5 }
m-6<=-2,2m-1>=5
解的3<=m<=4

Answer 2

A={x|x^2-3x-10≤0}
={x| (x-5)(x+2)≤0}
= { x| -2≤x≤5 }

A is subset of B
=> 2m-1 > 5 and m-6< -2
m> 3 and m<4
ie 3<m<4