Question

Решите неравенство.......................................

Answer 1

1)x<-2
(2x²+6x+6x+12-9)/(x²+2x+3)-1≤0
(2x²+12x+3-x²-2x-3)/(x²+2x+3)≤0
(x²+10x)≤0,т.к.x²+2x+3>0 при любом х,D<0
x(x+10)≤0
x=0 U x=-10
-10≤x≤0 U x<-2
x∈[-10;-2)
2)x≥-2
(2x²+6x-6x-12-9)/(x²+2x+3)-1≤0
(2x²-21-x²-2x-3)/(x²+2x+3)≤0
x²-2x-24≤0
x1+x2=2 U x1*x2=-24⇒x1=-4 u x2=6
-4≤x≤6 U x≥-2
x∈[-2;6]
Ответ x∈[-10;6]