Question

Решить систему уравнений :
$left { {{x+y+xy=11} atop {x^2y+xy^2=30}} right.$

Answer 1

$left { {{x+y+xy=11} atop {xy(x+y)=30}} right.$
Пусть: x+y = a , xy = b
Тогда:
$left { {{a+b=11} atop {ab=30}} right.$
$left { {{a=11-b} atop {(11-b)b=30}} right.$
$11b- b^{2} =30$
$b^{2} -11b+30=0$
$(b-6)(b-5)=0$
$b_{1} =6$   $b_{2} =5$
$a_{1} =5$   $a_{2} =6$

$1) left { {{x+y=5} atop {xy=6}} right.$
$2) left { {{x+y=6} atop {xy=5}} right.$

Ответ: (2;3). (1;5)