Question

log2(x2−3x)=2 . Выбери все корни уравнения

Answer 1

log₂(x² - 3x) = 2

D(y)

x² - 3x > 0

x · (x - 3) > 0

x ∈ (-∞; 0) U (3; +∞)

Решение

log₂(x² - 3x) = log₂4

x² - 3x = 4

x² - 3x - 4 = 0

D = b² - 4ac = 9 + 16 = 25 = 5²

x₁₂ = (3 ± 5) / 2 = 4; -1

Проверка

log₂(x² - 3x) = log₂(4² - 3 · 4) = log₂(16 - 12) = log₂4 = 2

log₂(x² - 3x) = log₂(1² - 3 · (-1)) = log₂(1 + 3) = log₂4 = 2

Ответ

4; -1