Question

Розв’язком системи рівнянь є {1/x-1/y=1/6 1/x+1/y=7/12

Answer 1

Ответ:

$\displaystyle {\displaystyle{\begin{cases} \frac{1}{x} - \frac{1}{y} = \frac{1}{6} \\ \frac{1}{x} + \frac{1}{y} = \frac{7}{12} \end{cases}}} \: \: \: = > {\displaystyle{\begin{cases} \frac{1}{x} = \frac{1}{6} + \frac{1}{y} \\ \frac{1}{x} + \frac{1}{y} = \frac{7}{12} \end{cases}}}$

$\displaystyle (\frac{1}{6} + \frac{1}{y} ) + \frac{1}{y} = \frac{7}{12}$

$\displaystyle \frac{1}{6} + \frac{2}{y } = \frac{7}{12} \\ \frac{2}{y} = \frac{7}{12} - \frac{1}{6} \\ \frac{2}{y} = \frac{5}{12} \\ y = \frac{12 \times 2}{5} \\ y = 4.8$

$\frac{1}{x} = \frac{1}{6} + \frac{1}{4.8} \\ \frac{1}{x} = \frac{3}{8} \\ x = \frac{8}{3}$