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

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moneybird
 3 years ago
Best ResponseYou've already chosen the best response.2\[\frac{y}{xz}=\frac{x+y}{z}=\frac{x}{y}\]

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.2Should I post the solution?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0\[a=\frac{x}{y}\]\[\frac{x+y}{z}=\frac{x}{y}\]\[z=\frac{y(x+y)}{x} \ \ \star\]plugging \(\star\) in\[\frac{y}{xz}=\frac{x}{y}\]gives\[\frac{y}{x\frac{y(x+y)}{x}}=\frac{x}{y}\]\[y^2=x^2xyy^2\]\[2\frac{y^2}{x^2}=1\frac{y}{x}\]\[\frac{2}{a^2}=1\frac{1}{a}\]\[a^2a=2\]
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