解不等式x^2-(2m+1)x+m^2+m

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解不等式x^2-(2m+1)x+m^2+m

解不等式x^2-(2m+1)x+m^2+m
解不等式x^2-(2m+1)x+m^2+m

解不等式x^2-(2m+1)x+m^2+m
1 -m
×
1 -(m+1)
(x-m)[x-(m+1)]

x²-(2m+1)x+m²+m<0
x²-(2m+1)x+m²+m
= x²-(2m+1)x+[(2m+1)/2] ²-[(2m+1)/2] ²+m²+m
=(x-m-1/2)²- m²-m-1/4+m²+m
=(x-m-1/2)² -1/4<0
(x-m-1/2)² <1/4
-1/2< x-m-1/2<1/2
m < x <1+ m