Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 732

a) 3x² – 3x – 17 = x + 3x² + 1
3x² – 3x – 17 – x – 3x² – 1 = 0
–4x – 18 = 9
–4x = 18
x = –4,5

б) 2x – (x² – 4) = 5 – (x² – 2x + 1)
2x – x² + 4 = 5 – x² + 2x – 1
2x – x² + x² – 2x = 5 – 1 – 4
0x = 0
x – любое число

в) 5(3x + 1) = 2(2x – 3)
15x + 5 = 4x – 6
15x – 4x = –6 – 5
11x = –11
x = –1

г) х – 3 + 6x = 2(2x – 1) – 3(4 – x)
7x – 3 = 4x – 2 – 12 + 3x
7x – 4x – 3x = –14 + 3
0x = –11
корней нет

д) $$\frac{(2 - х^2)}{3}$$ - 2х = $$\frac{(7 + 2х^2)}{5}$$
5(2 – x)² – 2x · 15 = 3(7 + 2x)²
20 – 20x + 5x² – 30x = 147 + 84x + 12x²
20 – 50x + 5x² – 147 – 84x – 12x² = 0
-7x² – 134x – 127 = 0
7x² + 134 + 127 = 0
D₁ = 67² – 7 · 127 = 4489 – 889 = 3600
x = $$\frac{-67 ± \sqrt{3600}}{7}$$ = -67 ± 60/7
x₁ = –1; x₂ = –127/7 = –181/7
Ответ: –1 и –181/7

е) $$\frac{(6 - х)^2}{8}$$ + х = 7 - $$\frac{(2х - 1)^2}{3}$$
3(6 – x)² + 24x = 7 · 24 – 8(2x – 1)²
108 – 36x + 3x² + 24x = 168 – 32x² + 32x – 8
108 – 12x + 3x² – 160 + 32x² – 32x = 0
35x² – 44x – 52 = 0
D₁ = (–22)² – 35 · (–52) = 484 + 1820 = 2304
x = $$\frac{22 ± \sqrt{2304}}{35}$$ = 22 ± 48/35
x₁ = 2; x₂ = –26/35
Ответ: 2 и –26/35