Question

алгебра 9 клас завдання​

Answer 1

х ≠ 0

х ≠ 6

х ≠ - 6

$\frac{12 - x}{ {x}^{2} + 6x } + \frac{3}{ {x}^{2} - 6x } = \frac{6}{ {x}^{2} - 36} \\ \frac{12 - x}{x(x + 6)} + \frac{3}{x(x - 6)} - \frac{6}{(x - 6)(x + 6)} = 0 \\ \frac{(12 - x)(x - 6) + 3(x + 6) - 6x}{x(x - 6)(x + 6)} = 0 \\ \frac{12x - 72 - {x}^{2} + 6x + 3x + 18 - 6x}{x(x - 6)(x + 6)} = 0 \\ \frac{ - {x}^{2} + 15x - 54 }{x(x - 6)(x + 6)} = 0 \\ - {x}^{2} + 15x - 54 = 0 \\ {x}^{2} - 15x + 54 = 0$

По теореме Виета:

${x}^{2} + bx + c = 0 \\ x _{1} + x_{2} = - b \\ x _{1} x_{2} = c$

${x}^{2} - 15x +5 4 = 0 \\ x _{1} + x_{2} = 15\\ x _{1} x_{2} = 54\\ x_{1} =6 \\ x_{2} = 9$

Первый корень не подходит

Ответ: х = 9