Question

Rezolva inecuatiile:

1) x²+3x+2≥0
2) 2x≤ x²
3) 4x²≤1
4) (x-3)(x+7)≥0
5) x²-x+3≥0

Answer 1

1) x²+3x+2≥0
x²+2x+x+2≥0
x(x+2)+(x+2)≥0
(x+2)(x+1)≥0
x∈(-∞, - 1)U(-2,+∞)
2) 2x≤ x²
x(2-x)≤0
x∈(-∞, 0)U(2,+∞)
3) 4x²≤1
4x²-1≤0
(2x-1) (2x+1)≤0
x∈(-1/2,+1/2)
4) (x-3)(x+7)≥0
x∈(-∞, - 7)U(3,+∞)
5) x²-x+3≥0
Deoarece Δ<0, x∈R