1) 4/х < x
ОДЗ: х≠0
4 - х <0<br>x
4-x² <0<br> x
-x(x² -4)<0<br>x(x-2)(x+2)>0
x=0 x=2 x= -2
- + - +
--------- -2 ------------- 0 ----------- 2 ----------
\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\
x∈(-2; 0)U(2; +∞)
2. 2+2x >2
x-3
ОДЗ: х≠3
2+2x - 2 > 0
x-3
2+2x-2(x-3)>0
x-3
2+2x-2x+6 > 0
x-3
8 > 0
x-3
x-3>0
x>3
x∈(3; +∞)
3.
7x⁴ - 2x² -5 <0<br>Пусть x² =y
7y² -2y -5<0<br>7y² -2y-5=0
D=4 +140=144
y₁ = 2-12 = -10/14 = -5/7
14
y₂ = 2+12 =1
14
+ - +
----------- -5/7 ----------- 1 --------------
\\\\\\\\\\\\\\
y∈(-5/7; 1)
х² > -5/7
x - любое число
x²<1<br>x² -1<0<br>(x-1)(x+1)<0<br>x=1 x= -1
+ - +
----------- -1 -------------- 1 --------------
\\\\\\\\\\\\\\\\
x∈(-1; 1)
Ответ: (-1; 1)