Question

Como se resuelve este ejercicio

Answer 1

Hola!

$\\ \frac{1}{x} + \frac{1}{y} = \frac{9}{20} \\ \frac{x + y}{xy} = \frac{9}{20} \\ x + y = \frac{9xy}{20}$

${x}^{2} y + x {y}^{2} = 180 \\ xy(x + y) = 180 \\ xy( \frac{9xy}{20} ) = 180 \\ 9 {x}^{2} {y}^{2} = 3600 \\ {x}^{2} {y}^{2} = 400 \\ xy = 20$

Si: xy = 20

$\\ x + y = \frac{9xy}{20} \\ x + y = 9 \frac{20}{20} \\ x + y = 9$

Por lo tanto:

x = 5

y = 4