Question

решить систему решить систему

Answer 1

$\left \{ {{2x+2y=18,} \atop { \frac{18}{x}- \frac{18}{y} = \frac{54}{60}; }} \right. \\ \left \{ {{x+y=9,} \atop { \frac{1}{x}- \frac{1}{y} = \frac{1}{20};}} \right. \\ \left \{ {{x=9-y,} \atop { \frac{1}{9-y}- \frac{1}{y} = \frac{1}{20};}} \right. \\ \left \{ {{x=9-y,} \atop {\frac{2y-9}{9y-y^2} = \frac{1}{20};}} \right. \\ \left \{ {{x=9-y,} \atop {9y-y^2=40y-180;}} \right. \\ \left \{ {{x=9-y,} \atop {y^2+31y-180=0;&(1)}} \right.$
Решим $(1)$:
$y^2+31y-180=0,\\ D=961+720=1681=41^2,\\ y= \frac{-31\pm41}{2},\\ \left[\begin{array}{ccc}y=5,\\y=-36;\end]$
Вернемся к системе:
$\left \{ {{x=4,} \atop {y=5;}} \right.$ или $\left \{ {{x=45}, \atop {y=-36.}} \right.$.