Question

Допоможіть будь ласка

Answer 1

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
x²+8x+15=0   D=4
x₁=-5     x₂=-3
(x+5)(x+3)<0
-∞_______+______-5_______+_______-3_______-_______+∞
x∈(-5;-3).
17.
(6x-1)(6x+1)-(12x-5)(x+2)<7-3x
36x²-1-(12x²+19x-10)-7+3x<0
36x²-1-12x²-19x+10-7+3x<0
24x²-16x+2<0   |÷2
12x²-8x+1<0
12x²-8x+1=0   D=16
x₁=1/6    x₂=1/2
(x-1/6)(x-1/2)<0
-∞_____+______1/6_____-______1/2______+______+∞
x∈(1/6;1/2).