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Для преобразования первого уравнения к формуле полного квадрата прибавим и отнимем от левой части 1 уравнения 2ху.
![left { {{x^2+y^2=25} atop {xy=12}} right. left { {{x^2+y^2=25} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx%5E2%2By%5E2%3D25%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{x^2+y^2+2xy-2xy=25} atop {xy=12}} right. left { {{x^2+y^2+2xy-2xy=25} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx%5E2%2By%5E2%2B2xy-2xy%3D25%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{(x+y)^2=25+2xy} atop {xy=12}} right. left { {{(x+y)^2=25+2xy} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7B%28x%2By%29%5E2%3D25%2B2xy%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{(x+y)^2=25+24} atop {xy=12}} right. left { {{(x+y)^2=25+24} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7B%28x%2By%29%5E2%3D25%2B24%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{(x+y)^2=49} atop {xy=12}} right. left { {{(x+y)^2=49} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7B%28x%2By%29%5E2%3D49%7D+atop+%7Bxy%3D12%7D%7D+right.+)
1)![x+y=7 x+y=7](https://tex.z-dn.net/?f=x%2By%3D7)
![left { {{x+y=7} atop {xy=12}} right. left { {{x+y=7} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx%2By%3D7%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{y=7-x} atop {xy=12}} right. left { {{y=7-x} atop {xy=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7By%3D7-x%7D+atop+%7Bxy%3D12%7D%7D+right.+)
![left { {{y=7-x} atop {x(7-x)=12}} right. left { {{y=7-x} atop {x(7-x)=12}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7By%3D7-x%7D+atop+%7Bx%287-x%29%3D12%7D%7D+right.+)
![left { {{y=7-x} atop {-x^2+7x-12=0}} right. left { {{y=7-x} atop {-x^2+7x-12=0}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7By%3D7-x%7D+atop+%7B-x%5E2%2B7x-12%3D0%7D%7D+right.+)
![left { {{y=7-x} atop {(3-x)(x-4)=0}} right. left { {{y=7-x} atop {(3-x)(x-4)=0}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7By%3D7-x%7D+atop+%7B%283-x%29%28x-4%29%3D0%7D%7D+right.+)
1.1)![x=3 x=3](https://tex.z-dn.net/?f=x%3D3)
![left { {{y=7-3=4} atop {x=3}} right. left { {{y=7-3=4} atop {x=3}} right.](https://tex.z-dn.net/?f=+left+%7B+%7B%7By%3D7-3%3D4%7D+atop+%7Bx%3D3%7D%7D+right.+)
1.2)![x=4 x=4](https://tex.z-dn.net/?f=x%3D4)
![left { {{y=7-4=3} atop {x=4}} right. left { {{y=7-4=3} atop {x=4}} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D7-4%3D3%7D+atop+%7Bx%3D4%7D%7D+right.+)
2)![x+y=-7 x+y=-7](https://tex.z-dn.net/?f=x%2By%3D-7)
![left { {{x+y=-7} atop {xy=12}} right. left { {{x+y=-7} atop {xy=12}} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7Bx%2By%3D-7%7D+atop+%7Bxy%3D12%7D%7D+right.)
![left { {{y=-x-7} atop {xy=12}} right. left { {{y=-x-7} atop {xy=12}} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-x-7%7D+atop+%7Bxy%3D12%7D%7D+right.)
![left { {{y=-x-7} atop {x(-x-7)=12}} right. left { {{y=-x-7} atop {x(-x-7)=12}} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-x-7%7D+atop+%7Bx%28-x-7%29%3D12%7D%7D+right.)
![left { {{y=-x-7} atop {-x^2-7x-12=0} right. left { {{y=-x-7} atop {-x^2-7x-12=0} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-x-7%7D+atop+%7B-x%5E2-7x-12%3D0%7D+right.)
![left { {{y=-x-7} atop {(-x-3)(x+4)=0} right. left { {{y=-x-7} atop {(-x-3)(x+4)=0} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-x-7%7D+atop+%7B%28-x-3%29%28x%2B4%29%3D0%7D+right.)
2.1)![x=-3 x=-3](https://tex.z-dn.net/?f=x%3D-3)
![left { {{y=-(-3)-7=-4} atop {x=-3} right. left { {{y=-(-3)-7=-4} atop {x=-3} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-%28-3%29-7%3D-4%7D+atop+%7Bx%3D-3%7D+right.)
2.2)![x=-4 x=-4](https://tex.z-dn.net/?f=x%3D-4)
![left { {{y=-(-4)-7=-3} atop {x=-4} right. left { {{y=-(-4)-7=-3} atop {x=-4} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7By%3D-%28-4%29-7%3D-3%7D+atop+%7Bx%3D-4%7D+right.)
Решение системы - 4 точки: (3,4); (4,3); (-3,-4); (-4,-3)
1)
1.1)
1.2)
2)
2.1)
2.2)
Решение системы - 4 точки: (3,4); (4,3); (-3,-4); (-4,-3)
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