403.
1) 8-4x ≤4
3x²-x-4
8-4x - 4 ≤0
3x²-x-4
8-4x-4(3x²-x-4) ≤0
3x²-x-4
8-4x-12x²+4x+16 ≤0
3x²-x-4
-12x²+24 ≤0
3x²-x-4
Разложим знаменатель на множитель:
3x²-x-4=0
D=1+4*3*4=49
x₁=1-7= -1
6
x₂=1+7=4/3
6
3x²-x-4=3(x+1)(x- 4/3)
- 12(x²-2) ≤0
3(x+1)(x- 4/3)
-4(x-√2)(x+√2) ≤0
(x+1)(x- 4/3)
(x-√2)(x+√2) ≥0
(x+1)(x- 4/3)
{x+1≠0
{x- 4/3≠0
{(x-√2)(x+√2)(x+1)(x- 4/3)≥0
x≠-1
x≠4/3
(x-√2)(x+√2)(x+1)(x- 4/3)≥0
x=√2 x=-√ x=-1 x=4/3
+ - + - +
--------- -√2 --------- -1 ------------ 4/3 --------------- √2 ----------------
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x∈(-∞; -√2] U (-1; 4/3) U [√2; +∞)