473)
4 + 21 / x = x
ОДЗ: x ≠ 0
4x + 21 = x²
x² - 4x - 21 = 0
По теореме Виета:
x1 * x2 = -21
x1 + x2 = 4
Тогда:
x1 = 7
x2 = -3
Ответ: x = 7
x = -3
479)
6 / x + 6 / (x + 1) = 5
6(x + 1) + 6x - 5x(x + 1) = 0
6x + 6 + 6x - 5x² - 5x = 0
-5x² + 7x + 6 = 0
5x² - 7x - 6 = 0
D = 49 + 5 * 4 * 6 = 169
x1 = (7 - 13) / 10 = -6 / 10 = -3 / 5
x2 = (7 + 13) / 10 = 20 / 10 = 2
Ответ: x = -0,6
x = 2