Question

已知全集U=R,集合A={x|（6/x+1）>=1},B={x|x2-2x-m<0}

若A∩B={x|-1<x<4},求实数m的值！

Answer 1

A={x| 6/(x+1）≥1 }
= { x| (5-x)/(x+1）≥ 0 }
= { x| -1<x≤5 }

B={x|x2-2x-m<0}
= {x| 1-√(1+4m)<x< 1+√(1+4m) }

if A∩B={x|-1<x<4}
=>1-√(1+4m)< -1 and 1+√(1+4m)≤ 4
=> 2 < √(1+4m) and √(1+4m) ≤ 3
=> 4 <1+4m and 1+4m ≤ 9
=> m > 3/4 and m≤ 2
=> 3/4<m≤ 2