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