อ้างอิง:
ข้อความเดิมเขียนโดยคุณ nong_jae
กำหนดให้
$x(y+z)=9$
$y(x+z)=7$
$z(x+y)=8$
จงหา $x:y:z$
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$x(y+z)=9.....1$
$x = \frac{9}{y+z}$....(*)
$y(x+z)=7.....2$
$y = \frac{7}{x+z}$....(*)
$z(x+y)=8.....3$
$z = \frac{8}{x+y}$....(*)
1-2:
$z = \frac{2}{x-y}$
$\frac{8}{x+y} = \frac{2}{x-y}$
$\frac{x}{y} = \frac{5}{3}$
1-3:
$y = \frac{1}{x-z}$
$\frac{7}{x+z} = \frac{1}{x-z}$
$\frac{x}{z} = \frac{4}{3}$
$\therefore \frac{y}{z} = \frac{4}{5}$
$\frac{x}{y} = \frac{5}{3}$
$\frac{y}{z} = \frac{4}{5}$
$\frac{x}{z} = \frac{4}{3}$
$\therefore x:y:z = 20:12:15$