Question

Решите ! желательно подробно! 240/x = 200/x-20 - 1

Answer 1

$\frac{240}{x} = \frac{200}{x - 20} - 1$
$\frac{240}{x} = \frac{200 - (x - 20)}{x - 20}$
x≠0; x≠20

$240(x - 20) = (220 - x) \times x$
$240x - 4800 = 220x - {x}^{2}$
${x}^{2} + 20x - 4800 = 0$

По теореме Виета:
{$x_{1} + x_{2} = - 20$
{$x_{1}x_{2} = - 4800$

[$x_{1} = 60$
[$x_{2} = - 80$
ответ: 60; -80.