Question

Este legat de Ecuatii, Inecuatii si Sisteme de ecuatii.
Va rog este foarte urgent!​

Answer 1

Răspuns:

1. -4≤3x+2≤4

-4≤3x+2;  -6≤3x /:3; x≥-2; x∈[-2; +∞)

3x+2≤4; 3x≤2; x≤$\frac{2}{3}$; x∈(-∞; $\frac{2}{3}$

x∈[-2; $\frac{2}{3}$

2. x²-5x+5≤1

x²-5x+4≤0; x²-x-4x+4≤0; x(x-4)-4(x-1)≤0; (x-1)(x-4)≤0

x-1=0; x₁=1

x-4=0; x₂=4

x₁+x₂=5

3. x²-5x+6≤0

x²-4x-x+4+2≤0; (x-2)²-(x-2)≤0; (x-2)(x-2-1)≤0; (x-2)(x-3)≤0

x-2=0; x₁=2

x-3=0; x₂=3

4. x²-9≤0

x²≤9 ⇒ x₁=3; x₂=-3

5. (x-1)²+x-7<0

x²-2x+1+x-7<0; x²-x-6<0; x(x-1)<6≤16 ⇒x₁=3; x₂=2

6. x(x-1)≤x+15

x²-x-x≤15   /+1; x²-2x+1≤16; (x-1)²≤16 ⇒

x₁-1=4; x₁=5

x₂-1=-4; x₂=-3

7. (x-1)(x-2)>x-3

x₂-3x+2>x-3; x²-4x+4>-1; (x-2)²>-1

dar,(x-2)²>-1, ∀ x∈R ⇒ (x-2)²>-1

8. (2x-1)²≤9

2x₁-1=3; 2x₁=4; x₁=2;

2x₂-1=-3; 2x₂=-2; x₂=-1

9. (x-2)(x+1)≤3(x+1)

x²-x-2≤3x+3; x²-4x-5≤0  /+9; x²-4x+4≤9; (x-2)²≤9 ⇒

x₁-2=3; x₁=5

x₂-2=-3; x₂=-1

10. (2x-1)(x+1)≤-x+11

2x²-x-1+x-11≤0; 2x²-12≤0   /:2 ⇒ x²≤6

x₁,₂=±$\sqrt{6}$

11. (x²-1)(x+1)≥0

x²-1≥0; x²≥1 ⇒ x₁,₂=±1

x+1≥0; x)≥-1 ⇒ x₃=-1

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