Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 749

а) 2(5х – 1)² + 35х – 11 = 0
Пусть 5х – 1 = t
35x – 7 = 7t
35x – 7 – 4 = 7t – 4
35y – 11 = 7t – 4
2t² + 7t – 4 = 0
D = 7² – 4 · 2 · (–4) = 49 + 32 = 81
t = $$\frac{-7 ± \sqrt{81}}{2 · 2}$$ = $$\frac{-7 ± \sqrt{9}}{4}$$
t₁ = 2/4 = 1/2 = 0,5; t₂ = –4
5x – 1 = 0,5    или    5x – 1 = –4
5x = 1,5                     5x = –3
x = 0,3                        x = –0,6

Ответ: –0,6; 0,3

б) (х² + х – 3)² + 12х² + 12х – 9 = 0
(x² + x – 3)² + 12(x + x – 3 + 3) – 9 = 0
(x² + x – 3)² + 12(x² + x – 3) + 36 – 9 = 0
пусть х² + х – 3 = t
t² + 12t + 27 = 0
по теореме Виета
t1 = –3; t2 = –9
x² + x – 3 = –3       или       x² + x – 3 = –9
x² + x – 3 + 3 = 0                x² + x – 3 + 9 = 0
x² + x = 0                             x² + x + 6 = 0
x(x + 1) = 0                          D = 1² – 4 · 1 · 6 = –23 < 0
x = 0 или x + 1 = 0             корней нет
                 x = –1

Ответ: 0, 1