15.
2*(x²+2)≥x*(x+5)
2x²+4≥x²+5x
x²-5x+4≥0
x²-5x+4=0 D=9
x₁=4 x₂=1 ⇒
(x-4)(x-1)≥0
-∞_____+_____1______-______4______+______+∞
x∈(-∞;1]U[4;+∞)
16.
x-(x+4)(x+5)>-5
x-(x²+9x+20)>-5
-x²-8x-20>-5
x²+8x+15<0<br>x²+8x+15=0 D=4
x₁=-5 x₂=-3
(x+5)(x+3)<0<br>-∞_______+______-5_______+_______-3_______-_______+∞
x∈(-5;-3).
17.
(6x-1)(6x+1)-(12x-5)(x+2)<7-3x<br>36x²-1-(12x²+19x-10)-7+3x<0<br>36x²-1-12x²-19x+10-7+3x<0<br>24x²-16x+2<0 |÷2<br>12x²-8x+1<0<br>12x²-8x+1=0 D=16
x₁=1/6 x₂=1/2
(x-1/6)(x-1/2)<0<br>-∞_____+______1/6_____-______1/2______+______+∞
x∈(1/6;1/2).