Question

Решите уравнение 6*5^x -6^x =4*6^x+1 -6*5^x+1

Answer 1

6*5ˣ - 6ˣ = 4*6ˣ⁺¹ - 6*5ˣ⁺¹
6*5ˣ - 6ˣ = 4*6ˣ *6¹ - 6*5ˣ * 5¹
6*5ˣ - 6ˣ = 4*6 * 6ˣ - 6*5 * 5ˣ
6*5ˣ - 6ˣ = 24*6ˣ - 30*5ˣ
6*5ˣ + 30*5ˣ = 24*6ˣ + 6ˣ
5ˣ * (6 + 30) = 6ˣ * (24 + 1)
36 * 5ˣ = 25 * 6ˣ
(5/6)ˣ = 25/36
(5/6)ˣ = (5/6)²
x = 2

Проверка
6*5² - 6² = 4*6²⁺¹ - 6*5²⁺¹
6*25 - 36 = 4*216 - 6*125
150 - 36 = 864 - 750 
    114 = 114 верное равенство
Ответ: х = 2