Question

Решите уравнения (x+2)^2(x-5)^3=(x-5)(x+2)^4 и (2x+1)^3(2x-3)^5=(2x+1)^5(2x-3)^3

Answer 1

Ответ:

$1.\\(x+2)^{2}*(x-5)^{3} = (x-5)(x+2)^{4}\\(x+2)^{2}*(x-5)^{3}- (x-5)(x+2)^{4} = 0\\(x+2)^{2}*(x-5)^{3}*((x-5)^{2}-(x+2)^{2}) = 0\\(x+2)^{2} = 0; x = -2\\x - 5 = 0; x = 5\\(x-5)^{2}-(x+2)^{2} = 0; x = \frac{3}{2} \\\\Answer: x_{1} = -2, x_{2} = 5, x_{3} = \frac{3}{2}$

$2.\\(2x+1)^{3}*(2x - 3)^{5} = (2x+1)^{5}*(2x-3)^{3}\\(2x+1)^{3}*(2x - 3)^{5} - (2x+1)^{5}*(2x-3)^{3} = 0\\(2x+1)^{3}*(2x - 3)^{3} * ((2x-3)^{2}*(2x+1)^{2}) = 0\\(2x+1)^{3} = 0; x = -\frac{1}{2}\\(2x-3)^{3} = 0; x = \frac{3}{2}\\(2x-3)^{2}-(2x+1)^{2} = 0; x = \frac{1}{2}\\\\Answer: x_{1} = -\frac{1}{2}, x_{2} = \frac{1}{2}, x_{3} = \frac{3}{2}$