Решить систему уравнений :[latex] \left \{ {{x+y+xy=11} \atop {x^2y+xy^2=30}} \right. [/latex]

[latex] \left \{ {{x+y+xy=11} \atop {xy(x+y)=30}} \right. [/latex] Пусть: x+y = a , xy = b Тогда: [latex] \left \{ {{a+b=11} \atop {ab=30}} \right. [/latex] [latex] \left \{ {{a=11-b} \atop {(11-b)b=30}} \right. [/latex] [latex]11b- b^{2} =30[/latex] [latex] b^{2} -11b+30=0[/latex] [latex](b-6)(b-5)=0[/latex] [latex] b_{1} =6[/latex]   [latex] b_{2} =5[/latex] [latex] a_{1} =5[/latex]   [latex] a_{2} =6[/latex] [latex]1) \left \{ {{x+y=5} \atop {xy=6}} \right. [/latex] [latex]2) \left \{ {{x+y=6} \atop {xy=5}} \right. [/latex] Ответ: (2;3). (1;5)