4x(x-2)≤5; (2x+1)(x+1)≥3; 3x(1-x)≤-6; (1-2x)(1-3x)≤2

Question

4x(x-2)≤5;
(2x+1)(x+1)≥3;
3x(1-x)≤-6;
(1-2x)(1-3x)≤2

Answer 1

4x^2 - 8x <= 5<br>4x^2 - 8x - 5 <= 0<br>4x^2 - 8x - 5 = 0
D = 64+80=144 = 12^2
x1 = (8+12)/8 = 2,5
x2 = (8-12)/8 = -1/2

2x^2 + x + x + 1 >= 3
2x^2 + 2x - 2 >= 0
x^2 + x - 1 >= 0
D = 1 + 4 = 5
x1 = (-1 + sqrt5)/2
x2 = (-1 - sqrt5)/2