## moneybird 4 years ago If y / (x-z) = (x + y) / z = x / y for three distinct positive numbers x, y, and z, find x / y.

1. moneybird

$\frac{y}{x-z}=\frac{x+y}{z}=\frac{x}{y}$

2. moneybird

Should I post the solution?

3. mukushla

$a=\frac{x}{y}$$\frac{x+y}{z}=\frac{x}{y}$$z=\frac{y(x+y)}{x} \ \ \star$plugging $$\star$$ in$\frac{y}{x-z}=\frac{x}{y}$gives$\frac{y}{x-\frac{y(x+y)}{x}}=\frac{x}{y}$$y^2=x^2-xy-y^2$$2\frac{y^2}{x^2}=1-\frac{y}{x}$$\frac{2}{a^2}=1-\frac{1}{a}$$a^2-a=2$