Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 771

2xy = 10
xy = 5
x + 5 + y = 11
x + y = 6
x = 6 – y
6 – y + (6 – y)y + y = 11
6 – y + 6y – y² + y = 11
–y² + 6y – 5 = 0
y² – 6y + 5 = 0
по теореме Виета
y₁ = 1, y₂ = 5
x₁ = 6 – 1 = 5
x₂ = 6 – 5 = 1

Ответ: (5; 1) и (1; 5)

3x + y = 7
y = 7 – 3x
x + 2(7 – 3x) + x(7 – 3x) = –7
x + 14 – 6x + 7x – 3x² + 7 = 0
–3x² + 2x + 21 = 0
3x² – 2x – 21 = 0
D₁ = (–1)² – 3 · (–21) = 1 + 63 = 64
x = $$\frac{1 ± \sqrt{64}}{3}$$ = $$\frac{1 ± \sqrt{8}}{3}$$
x₁ = 3, x₂ = –7/3 = –21/3
y₁ = 7 – 3 · 3 = –2
y₂ = 7 – 3 · (–7/3) = 7 + 7 = 14

Ответ: (3; –2) и (–21/3; 14)

x² – 2xy + y² = 34 – 30
(x – y)² = 4

1)x – y = 2
x = y + 2
(y + 2)² + y² = 34
y² + 4y + 4 + y² = 34
2y² + 4y – 30 = 0
y² + 2y – 15 = 0
по теореме Виета
y₁ = 3, y₂ = –5
x₁ = 3 + 2 = 5
x₂ = –5 + 2 = –3

2)x – y = –2
x = y – 2
(y – 2)² + y² = 34
y² – 4y + 4 + y² = 34
2y² – 4y – 30 = 0
y² – 2y – 15 = 0
по теореме Виета
y₁ = –3, y₂ = 5
x₁ = –3 – 2 = –5
x₂ = 5 – 2 = 3

Ответ: (5; 3), (–3; –5), (–5; –3), (3; 5)

$$\frac{64}{у^2}$$ – y² = 12
64 – y⁴ – 12y² = 0
y⁴ + 12y² – 64 = 0
пусть y² = t
t² + 12t – 64 = 0
по теореме Виета
t₁ = –16, t₂ = 4
y² = 4        или        y² = –16
y₁ = 2, y₂ = –2        корней нет
x₁ = 8/2 = 4
x₂ = 8/–2 = –4

Ответ: (4; 2) и (–4; –2)