Вариант 1.
1.
а) 2a+3<5<br>2a<5-3<br>2a<2<br>a<1<br>
б) 1-b<2b+3<br>-b-2b<3-1<br>-3b<2<br>b>-2/3
2.
x²+3x+2>0
Парабола, ветви вверх.
x²+3x+2=0
D=9-8=1
x₁= -3-1 = -2
2
x₂ = -3+1 = -1
2
+ - +
------- -2 ------------ -1 --------------
\\\\\\\\ \\\\\\\\\\\\\\
x∈(-∞; -2) U (-1; +∞)
3.
{2x-6≤0
{x²+7x+6>0
2x-6≤0
2x≤6
x≤3
x²+7x+6>0
Парабола, ветви вверх.
x²+7x+6=0
D=49-24=25
x₁= -7 -5 = -6
2
x₂ = -7+5 = -1
2
+ - +
----------- -6 ----------- -1 -------------
\\\\\\\\\\ \\\\\\\\\\\\\\\\\\
x∈(-∞; -6)U(-1; +∞)
{x≤3
{x∈(-∞; -6)U(-1; +∞)
х∈(-∞; -6)U(-1; 3]
4. A=(-∞; -3)U(1; +∞)
В=[-4;2]
\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---------- -4 -------- -3 ------------ 1 ----------2 ---------------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
5.
√((x²-2x-8)/(16-x²))
{ x²-2x-8 ≥0
16-x²
{ 16-x²≠0
x² -2x-8 ≥ 0
16-x²
Разложим х²-2х-8 на множители:
x²-2x-8=0
D=4+32=36
x₁=2-6 = -2
2
x₂ = 2+6 =4
2
x²-2x-8 =(x+2)(x-4)
(x+2)(x-4) ≥0
-(x²-16)
(x+2)(x-4) ≤ 0
(x-4)(x+4)
x+2 ≤ 0
x+4
x≠-4
(x+2)(x+4)≤0
x= -2 x=-4
+ - +
--------4 ---------- -2 ------------
\\\\\\\\\\\\
x∈(-4; -2]
16-x²≠0
(4-x)(4+x)≠0
x≠4 x≠-4
D(y)=(-4; -2]