Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 587

9x² + 9y² + 18xy = 13 + 12
(3x)² + 2 · 3x · 3y + (3y)² = 25
(3x + 3y)² = 25
3x + 3y = ± 5
3y = ± 5 – 3x

1) x(5 – 3x) = 2
5x – 3x² – 2 = 0
3x² – 5x + 2 = 0
D = (–5)² – 4 · 3 · 2 = 25 – 24
х = $$\frac{5 ± \sqrt{1}}{2 \cdot 3}$$ = 5 ± 1/6

x₁ = 1; x₂ = 4/6 = 2/3

При х = 1
3y = 5 – 3 · 1
3y = 5 – 3
3y = 2
y = 2/3

При х = 2/3
3y = 5 – 3 · 2/3
3y = 5 – 2
3y = 3
y = 1

4) x(–5 – 3x) = 2
–5x – 3x² – 2 = 0
3x² + 5x + 2 = 0
D = 5² – 4 · 3 · 2 = 25 – 24 = 1

х = $$\frac{-5 ± \sqrt{1}}{2 \cdot 3}$$ = –5 ± 1/6

x1 = –2/3; x² = –1
При х = –2/3
3y = –5 – 3 · (–2/3)
3y = –5 + 2
3y = –3
y = –1

При х = –1
3y = –5 – 3 · (–1)
3y = –5 + 3
3y = –2
y = –2/3

Ответ: (2/3; 1); (–2/3; –1); (1; 2/3); (–1; –2/3)

1) x² + y² + 4x² – y² = 29 – 9
5x² = 20
x² = 4
x = ± 2

При x = –2
(–2)² + y² = 29
4 + y² = 29
y² = 25
y = ± 5

При x = 2
2² + y² = 29
4 + y² = 29
y = ± 5

Ответ: (2; 5); (–2; 5); (2; –5); (2; –5)

1) 3x² – 2x² + xy – xy – x = 6 – 6
x² – x = 0
x(x – 1) = 0
x = 0 или x = 1

При х = 0
2 · 0² + 0 · y = 6
0 = 6 – неверно

При х = 1
2 · 1² + 1 · y = 6
2 + 4 = 6
y = 4

Ответ: (1; 4)

1) 3x² – 3x² – 3y² + 2y² + 3y = 15 – 25
–y² + 3y = –10
y² – 3y – 10 = 0
D = (–3)² – 4 · 1 · (–10) = 9 + 40 = 49

у = $$\frac{3 ± \sqrt{49}}{2}$$ = 3 ± 7/2

y₁ = 5; y₂ = –2

При у = 5
3x² – 2 · 5² = 25
3x² – 50 = 25
3x² = 75
x² = 25
x = ± 5

При у = –2
3x² – 2 · (–2)² = 25
3x² – 8 = 25
3x² = 33
x² = 11
x = ± $$\sqrt{11}$$

Ответ: (–5; 5); (5; 5); ($$\sqrt{11}$$; –2); (–$$\sqrt{11}$$; –2)