Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 493

(y + 3)(y + 1) = 2y² + 8y + 3
y² + 3y + y + 3 – 2y² – 8y – 3 = 0
–y² – 4y = 0
–y(y + 4) = 0

–y = 0  или  у + 4 = 0
y₁ = 0           y₂ = –4

x₁ = 0 + 4 = 4
x₂ = –4 + 4 = 0

Ответ: (4; 0), (0; –4)

(2x + 2 + 1)(x – 1) = x² + x + 1
(2x + 3)(x – 1) – x² – x – 1 = 0
2x² + 3x – 2x – 3 – x² – x – 1 = 0
x² – 4 = 0
(x – 2)(x + 2) = 0

x – 2 = 0  или  х + 2 = 0
x₁ = 2               x₂ = –2

y₁ = 2 + 1 = 3
y₂ = –2 + 1 = –1

Ответ: (2; 3), (–2; –1)

(x + 1)(2x – 1) = 4x² – 10x – 1
2x² + 2x – x – 1 – 4x² + 10x + 1 = 0
–2x² + 11x = 0
x(–2x + 11) = 0
x₁ = 0  или  –2х + 11 = 0
                     –2х = –11
                      х = 5,5

y₁ = 2 · 0 – 5 = –5
y₂ = 2 · 5,5 – 5 = 6

Ответ: (0; –5), (5,5; 6)

–y(y + 5) – y² + 12 = 0
–y² – 5y – y² + 12 = 0
–2y² – 5y + 12 = 0
2y² + 5y – 12 = 0
D = 5² – 4 · 2 (–12) = 25 + 96 = 121

у = $$\frac{-5 ± \sqrt{121}}{2 \cdot 2}$$ = $$\frac{-5 ± \sqrt{11}}{4}$$

у₁ = –4, у₂ = 1,5
х₁ = 1 – (–4) = 5
х₂ = 1 – 1,5 = –0,5

Ответ: (5; –4), (–0,5; 1,5)