Question

помогите решить рациональным путем​

Answer 1

$\left \{ {{x^2+2xy+y^2-4x-4y-45=0,} \atop {x^2-2xy+y^2-2x+2y-3=0;}} \right. \Leftrightarrow \left \{ {{(x+y)^2-4(x+y)-45=0,} \atop {(x-y)^2-2(x-y)-3=0;}} \right. \Leftrightarrow\left \{ {{ \left [ {{x+y=9,} \atop {x+y=-5,}} \right. } \atop {\left [ {{x-y=3,} \atop {x-y=-1.}} \right. }} \right.$

1 случай:

$\left \{ {{x+y=9,} \atop {x-y=3;}} \right. \Leftrightarrow \left \{ {{x=6,} \atop {y=3.}} \right.$

2 случай:

$\left \{ {{x+y=9,} \atop {x-y=-1;}} \right. \Leftrightarrow \left \{ {{x=4,} \atop {y=5.}} \right.$

3 случай:

$\left \{ {{x+y=-5,} \atop {x-y=3;}} \right. \Leftrightarrow \left \{ {{x=1,} \atop {y=-4.}} \right.$

4 случай:

$\left \{ {{x+y=-5,} \atop {x-y=-1;}} \right. \Leftrightarrow \left \{ {{x=-3,} \atop {y=-2.}} \right.$

Ответ: (-3; -2), (1; -4), (4; 5), (6; 3).