(1)
mx+2=x.(1)
(m-2)x^2+(2m-3)x-1+m=0.(2)
(1)的根是负实数
(m-1)x=-2
x=-2/(m-1)0
m>1
(2)有实数根
Δ=(2m-3)^2-4(m-2)(-1+m)
=4m^2-12m+9-4m^2+12m-8
=1>0
m∈R
m的取值范围:(1,+∞)
(2)
两个方程的根为整数
x=-2/(m-1)为整数
m=2 x=-2/(2-1)=-2
m=3 x=-2/(3-1)=-1
对于第二个方程:
x=(3-2m±1)/[2(m-2)]
x1=(2-2m)/[2(m-2)]
=(1-m)/(m-2)
x2=(4-2m)/[2(m-2)]
=(2-m)/(m-2)
m≠2
∴m=3 x1=(1-3)/(3-2)=-2 x2=(2-3)/(3-2)=-1均为整数
综上,m=3