Відповіді на вправи: 477

1) 2x(3 – 4x) $\ge$ –2;

6x – 8x² + 2 $\ge$ 0 |• (–1);

8x² – 6x – 2 $\le$ 0;

8x² – 6x – 2 = 0;

D = (–6)² • 4 • 8 • (–2) = 100 =

= 10²;

x₁ = $\frac{6-10}{16}$ = $\frac{-4}{16}$ = –$\frac{1}{4}$ = –0,25;

x₂ = $\frac{6+10}{16}$ = $\frac{16}{16}$ = 1.

2) у(y – 10) $\le$ –21;

y² – 10y + 21 $\le$ 0;

y₁ = 3, y₂ = 7;

у $\in$ [3; 7].

x $\in$ [–0,25; 1].

3) x(x – 7) + 12 < 0;

x² – 7x + 12 < 0;

x² – 7x + 12 = 0;

x₁ = 3, x₂ = 4;

x $\in$ (3; 4).

4) у(y + 8) < 9;

y² + 8y – 9 < 0;

y² + 8y – 9 = 0;

y₁ = –9, y₂ = 1;

у $\in$ (–9; 1).