Відповіді на вправи: 467 (1-4)

1) x² $\le$ 1;

x² – 1 $\le$ 0;

x² – 1 = 0;

x² = 1;

x₁ = –1, x₂ = 1;

x $\in$ [–1; 1].

2) x² + 5x $\ge$ 0;

x² + 5x = 0;

x(x + 5) = 0;

x₁ = 0, x₂ = –5;

x $\in$ (–$\infty$; –5] $\cup$ [0; +$\infty$).

3) 4x² + 1 > 0;

4x² + 1 = 0;

4x² = –1;

x² = –$\frac{1}{4}$;

x₁ = –$\frac{1}{2}$, x₂ = $\frac{1}{2}$;

4) x² – 16 $\ge$ 0

x² – 16 = 0;

x² = 16;

x₁ = –4, x₂ = 4.

x $\in$ (–$\infty$; –4] $\cup$ [4; +$\infty$).

x $\in$ (–$\infty$; –$\frac{1}{2}$) $\cup$ ($\frac{1}{2}$; +$\infty$).

5) x² + 9 < 0;

x² + 9 = 0;

D < 0.

6) x² + 3 > 0;

x² + 3 = 0;

D < 0.

$\varnothing$.

x $\in$ (–$\infty$; +$\infty$).

7) x² – 8x $\le$ 0;

x² – 8x = 0;

x(x – 8) = 0;

x₁ = 0, x₂ = 8.

x $\in$ [0; 8].

8) x² – 4x > 0;

x² – 4x = 0;

х(x – 4) = 0;

x = 0, x – 4 = 0; x = 4.

x $\in$ (–$\infty$; 0) $\cup$ (4; +$\infty$).

9) 25x² $\ge$ 100;

x² – 4 $\ge$ 0;

x² – 4 = 0;

x² = 4;

x₁ = –2, x₂ = 2.

x $\in$ (–$\infty$; –2] $\cup$ [2; +$\infty$).

10) 4x² – 8х < 0;

4x² – 8х = 0;

х(4x – 8) = 0;

x = 0, 4x – 8 = 0;

4x = 8; х = 2.

x $\in$ (0; 2).