Question

Решите номер 11.Есть вложение.

Answer 1

$\left \{ {{x-y=20} \atop { \frac{1}{x} - \frac{1}{y}= \frac{4}{15} }} \right. \\\ \left \{ {{y-x=-20} \atop { \frac{y-x}{xy}= \frac{4}{15} }} \right. \\\ \left \{ {{y-x=-20} \atop { \frac{-20}{xy}= \frac{4}{15} }} \right. \\\ \left \{ {{y-x=-20} \atop { -\frac{5}{xy}= \frac{1}{15} }} \right. \\\ \left \{ {{y=x-20} \atop { xy= -75 }} \right. \\\ x(x-20)= -75 \\\ x^2-20x+75=0 \\\ D_1=10^2-75=25 \\\ x_1=10+5=15\Rightarrow y_1=15-20=-5 \\\ x_2=10-5=5\Rightarrow y_2=5-20=-15$
Ответ: (15; -5); (5; -15)