Відповіді до завдань § 12 - § 14: 12.21 (1-2)

1) х² + 8х + 16 < 0;

у = х² + 8х + 16;

х² + 8х + 16 = 0;

D = 64 – 64 = 0;

х₁ = х₂ = 4.

х ∈ ∅.

2) 25х² – 10х + 1 ≥ 0;

у = 25х² – 10х + 1;

25х² – 10х + 1 = 0;

D = 100 – 100 = 0;

x₁ = x₂ = $\frac{10}{50}$ = $\frac{1}{5}$.

x ∈ (–∞; +∞).

3) 9 – 6х + х² ≤ 0;

у = 9 – 6х + х²;

х² – 6х + 9 = 0;

х₁ = х₂ = 3.

х = 3.

4) 100х² – 120x + 36 > 0;

у = 100x2 – 120x + 36;

100х2 – 120x + 36 = 0;

D = 14400 – 4 • 10 • 36 = 14400 – 14400 = 0;

x₁ = x₂ = $\frac{120}{200}$ = $\frac{3}{5}$.

x ∈ (–∞; 0,6) ∪ (0,6; +∞).

5) 2x – x² – 1 ≥ 0;

у = –х² + 2х – 1;

x² – 2х + 1 = 0;

х₁ = х₂ = 1.

х = 1.

6) –64x² – 112x – 49 ≤ 0;

у = –64x² – 112x – 49;

64x² + 112x + 49 = 0;

D = 12544 – 4 • 64 • 49 = 12544 – 12544 = 0;

x₁ = x₂ = $\frac{112}{64•2}$ = $\frac{112}{128}$ = $\frac{7}{8}$.

x ∈ (–∞; +∞).

7) –36x² + 60x – 25 > 0;

у = –36x² + 60x – 25;

36x² – 60x + 25 = 0;

D = 3600 – 4 • 36 • 25 = 3600 – 3600 = 0;

x₁ = x₂ = $\frac{60}{72}$ = $\frac{5}{6}$.

x ∈ ∅.

8) –x² + 16x – 64 < 0;

у = –x² + 16 – 64;

x² – 16x + 64 = 0;

x₁ = x₂ = 8.

x ∈ (–∞; 8) ∪ (8; +∞).