x = 9
Объяснение:
12ₓ * 33ₓ = 406ₓ
(1 * x¹ + 2 * x⁰) * (3 * x¹ + 3 * x⁰) = 4 * x² + 0 * x¹ + 6 * x⁰
(1 * x + 2 * 1) * (3 * x + 3 * 1) = 4 * x² + 0 * x + 6 * 1
(x + 2) * (3x + 3) = 4x² + 6
3x² + 6x + 3x + 6 = 4x² + 6
4x² - 3x² - 6x - 3x = 6 - 6
x² - 9x = 0
x * (x - 9) = 0
x - 9 = 0 или x = 0 (не подходит)
x = 9
Проверка:
12₉ = 1 * 9¹ + 2 * 9⁰ = 9 + 2 = 11₁₀
33₉ = 3 * 9¹ + 3 * 9⁰ = 27 + 3 = 30₁₀
406₉ = 4 * 9² + 0 * 9¹ + 6 * 9⁰ = 324 + 0 + 6 = 330₁₀
11 * 30 = 330
