1) 4 = 20x - 25x²
-25x² + 20x - 4 = 0 | * (-1)
25x² - 20x + 4 = 0
D = b² - 4ac = (-20)² - 4 * 25 * 4 = 400 - 400 = 0
x = - b / 2a = 20 / 50 = 0.4
ответ. 0.4
2) 2x = x² | :2
x = x²
x - x² = 0
x (1 - x) = 0
x = 0 или 1 - x = 0
x = 1
ответ. 0; 1
3) 21x + 9x² + 10 = 0
9x² + 21x + 10 = 0
D = b² - 4ac = 21² - 4 * 9 * 10 = 441 - 360 = 81 = 9²
x1,2 = -b ± √D / 2a = -21 ± 9 / 18
x1 = -2/3
x2 = -5/3
ответ. -2/3; -5/3
4) 4x² = 36
x² = 36 / 4
x² = 9
x1,2 = ±3
ответ. ±3
5) 5 + 4x + x² = 0
x² + 4x + 5 = 0
D = b² - 4ac = 4² - 4 * 1 * 5 = 16 - 20 = - 4
D < 0, ур-е не имеет решений
ответ. нет корней
6) x² - 12x + 32 = 0
D = b² - 4ac = (-12)² - 4 * 1 * 32 = 144 - 128 = 16 = 4²
x1,2 = - b ± √D / 2a = 12 ± 4 / 2
x1 = 8
x2 = 4
ответ. 8; 4
7) 5 - 3a² - 2a = 0
-3a² - 2a + 5 = 0 | * (-1)
3a² + 2a - 5 = 0
D = b² - 4ac = 2² - 4 * 3 * (-5) = 4 + 60 = 64 = 8²
a1,2 = -b ± √D / 2a = -2 ± 8 / 6
a1 = 1
a2 = -5/3
ответ. 1; -5/3
