Problem
ALG-B1-M10-P013 Fraction equation
#13
★★★☆☆ Level 3 of 5
Find positive integer solutions of \(\frac{1}{x}+\frac{1}{y}=\frac{1}{8}\).
Transform it to \((x-8)(y-8)=64\).
From \(8x+8y=xy\), we get \((x-8)(y-8)=64\). Positive divisors of \(64\) are \(1,2,4,8,16,32,64\). Thus the solutions are \((9,72),(10,40),(12,24),(16,16)\) and the symmetric pairs.
The template of completing to a product.