7) 7x² = (2x + 1)² + 3x² - 5
7x² = 4x² + 4x + 1 + 3x² - 5
7x² = 7x² + 4x - 4
4x - 4 = 0
4x = 4
x = 1
Ответ: x = 1.
8) (x + 3)(x - 2) - (x - 3)(x + 2) - 5 = 6x - 7
(x² - 2x + 3x - 6) - (x² + 2x - 3x - 6) - 5 = 6x - 7
x² + x - 6 - x² + x + 6 - 5 = 6x - 7
2x - 5 = 6x - 7
6x - 2x = -5 + 7
4x = 2
x = 0,5
Ответ: x = 0,5.
10) x³ + 2x² - 9x - 18 = 0
x²(x + 2) - 9(x + 2) = 0
(x² - 9)(x + 2) = 0
(x - 3)(x + 3)(x + 2) = 0
x - 3 = 0 ⇒ x = 3
x + 3 = 0 ⇒ x = -3
x + 2 = 0 ⇒ x = -2
Ответ: x = -3; -2; 3.
12) (5 - x)² - (3x - 2)(2x + 1) = x(2 - 5x)
25 - 10x + x² - (6x² + 3x - 4x - 2) = 2x - 5x²
25 - 10x + x² - 6x² + x + 2 = 2x - 5x²
-5x² + 27 - 9x = 2x - 5x²
27 - 9x = 2x
11x = 27
x = 27/11 = 2 6/11
Ответ: x = 27/11.
14) 2|x - 1| - 3x - 5 = 2 - 2(3x - 1) - 2x
2|x - 1| - 3x - 5 = 2 - 6x + 2 - 2x
2|x - 1| - 3x - 5 = 4 - 8x
2|x - 1| - 3x + 8x = 4 + 5
2|x - 1| + 5x = 9
1. Раскрываем со знаком "+" (x ≥ 1):
2(x - 1) + 5x = 9
2x - 2 + 5x = 9
7x = 9 + 2
x = 11/7
2. Со знаком "-" (x < 1):
-2(x - 1) + 5x = 9
-2x + 2 + 5x = 9
3x = 7
x = 7/3 - не подходит
Ответ: x = 11/7.