Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 770

x² + 2x + 8 – 2x² = 0
–x² + 2x + 8 = 0
x² – 2x – 8 = 0
по теореме Виета
x₁ = 4, x₂ = –2
y₁ = 2 · 4 = 8
y₂ = 2 · (–2) = –4

Ответ: (4; 8) и (–2; –4)

x² – 64 + 16x – x² – 16 = 0
16x = 80
x = 5
y = 8 – 5 = 3

Ответ: (5; 3)

25 – 10y + y² – 5y + y² + y² – 13 = 0
3y² – 15y + 12 = 0
y² – 5y + 4 = 0
по теореме Виета
y₁ = 1, y₂ = 4
x₁ = 5 – 1 = 4
x₂ = 5 – 4 = 1

Ответ: (4; 1) и (1; 4)

9y² + y² – 9y² = 1
y² = 1
y² = 1
y₁ = 1, y₂ = –1
x₁ = –3 · 1 = –3
x₂ = –3 · (–1) = 3

Ответ: (–3; 1) и (3; –1)

2x² + 5x – 10,5x – 12 + 12 = 0
2x² – 5,5x = 0
x(2x – 5,5) = 0
x = 0  или  2x – 5,5 = 0
                    2x = 5,5
                    x = 2,75
y₁ = 3,5 · 0 + 4 = 4
y₂ = 3,5 · 2,75 + 4 = 13,625

Ответ: (0; 4) и (2,75; 13,625)

16x² – 16x + 4 – 2x – 2 = 0
16x² – 18x + 2 = 0
8x² – 9x + 1 = 0
D = (–9)² – 4 · 8 · 1 = 81 – 32 = 49
x = $$\frac{9 ± \sqrt{49}}{2 \cdot 8}$$ = $$\frac{9 ± \sqrt{7}}{16}$$
x₁ = 1, x₂ = 2/16 = 1/8
y₁ = 4 · 1 – 2 = 2
y₂ = 4 · 1/8 – 2 = –11/2

Ответ: (1; 2) и (1/8; –11/2)