Question

Решите пожалуйста два уравнения.

Answer 1

Ответ:

1) x = 101; 2) x1 = 1, x2=1/3

Пошаговое объяснение:

$1) t = lg(x-1)\\\\t = |x-101|+2\\\\\left \{ {{t = x-101+2=x-99} \atop {t = 101 - x + 2=103-x}} \right. \\\\x-99 = 103-x = > 2x = 202; x = 101\\lg(x-1) = lg(101-1) = lg(100) = 2\\\\\\4x - |x -2| -3 = 0\\a) -(x-2) = 4x - 3\\-x+2 = 4x -3 = > -5x = -5 = > x=1\\b) x-2 = 4x-3\\x-4x = -3+2\\-3x = -1\\x = \frac{1}{3}$