Question

1) x - y = 6, x + xy = -4; x + y = 9, 2) x + y2 = 29; 3​

Answer 1

Ответ:

Пошаговое объяснение:

1)

$\left \{ {{x-y=6} \atop {x+xy=-4}} \right;\\\left \{ {{x=6+y} \atop {x+xy=-4}} \right. \\\left \{ {{x=6+y} \atop {6+y+(6+y)*y=-4}} \right. \\\\6+y+6y+y^2+4=0;\\y^2+7y+10=0;$

по т.Виета:

(y+5)*(y+2)=0;

$y_{1}= -5; y_{2}=-2;\\ x_{1}=6-5=1;\\ x_{2}=6-2=4;$

Ответ:

$\left \{ {{x_{1} =1} \atop {y_{1} =-5}} \right. ;\\\left \{ {{x_{2} =4} \atop {y_{2} =-2}} \right.$

2)

$\left \{ {{x+y=9} \atop {x+y^2=29}} ;\\\left \{ {{x=9-y} \atop {x+y^2=29}} ;\\9-y+y^2=29;\\y^2-y-20=0;$

По т.Виета:

(у-5)(у+4)=0;

$y_{1}= 5; y_{2}=-4;\\ x_{1}=9-5=4;\\ x_{2}=9+4=13;$

Ответ:

$\left \{ {{x_{1} =4} \atop {y_{1} =5}} \right. ;\\\left \{ {{x_{2} =13} \atop {y_{2} =-4}} \right.$