Ответы
Ответ дал:
15
Обработаем второе уравнение
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![3x^2-2y^2+5xy-17x-6y+20=0\\3x^2-2y^2-xy+6xy-5x-12x-10y+4y+20=0\\ x(3x-y-5)+2y(3x-y-5)-4(3x-y-5)=0\\ (3x-y-5)(x+2y-4)=0 3x^2-2y^2+5xy-17x-6y+20=0\\3x^2-2y^2-xy+6xy-5x-12x-10y+4y+20=0\\ x(3x-y-5)+2y(3x-y-5)-4(3x-y-5)=0\\ (3x-y-5)(x+2y-4)=0](https://tex.z-dn.net/?f=3x%5E2-2y%5E2%2B5xy-17x-6y%2B20%3D0%5C%5C3x%5E2-2y%5E2-xy%2B6xy-5x-12x-10y%2B4y%2B20%3D0%5C%5C+x%283x-y-5%29%2B2y%283x-y-5%29-4%283x-y-5%29%3D0%5C%5C+%283x-y-5%29%28x%2B2y-4%29%3D0)
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Также упростим первое уравнение
![10x^2-2xy-38x+41-6y+5y^2=0\\ 10x^2+10x(-0.2y-3.8)+41-6y+5y^2=0\\ 10(x-0.1y-1.9)^2+(-(0.1y^2+3.8y+36.1)+41-6y+5y^2)=0\\10(x-0.1y-1.9)^2+4.9(y-1)^2=0 10x^2-2xy-38x+41-6y+5y^2=0\\ 10x^2+10x(-0.2y-3.8)+41-6y+5y^2=0\\ 10(x-0.1y-1.9)^2+(-(0.1y^2+3.8y+36.1)+41-6y+5y^2)=0\\10(x-0.1y-1.9)^2+4.9(y-1)^2=0](https://tex.z-dn.net/?f=10x%5E2-2xy-38x%2B41-6y%2B5y%5E2%3D0%5C%5C+10x%5E2%2B10x%28-0.2y-3.8%29%2B41-6y%2B5y%5E2%3D0%5C%5C+10%28x-0.1y-1.9%29%5E2%2B%28-%280.1y%5E2%2B3.8y%2B36.1%29%2B41-6y%2B5y%5E2%29%3D0%5C%5C10%28x-0.1y-1.9%29%5E2%2B4.9%28y-1%29%5E2%3D0)
Получаем
![\left \{ {{10(x-0.1y-1.9)^2+4.9(y-1)^2=0} \atop {3x-y-5=0}} \right. \to \left \{ {{y-1=0} \atop {3x-y-5=0}} \right. \to \left \{ {{y=1} \atop {x=2}} \right. \left \{ {{10(x-0.1y-1.9)^2+4.9(y-1)^2=0} \atop {3x-y-5=0}} \right. \to \left \{ {{y-1=0} \atop {3x-y-5=0}} \right. \to \left \{ {{y=1} \atop {x=2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B10%28x-0.1y-1.9%29%5E2%2B4.9%28y-1%29%5E2%3D0%7D+%5Catop+%7B3x-y-5%3D0%7D%7D+%5Cright.+%5Cto++%5Cleft+%5C%7B+%7B%7By-1%3D0%7D+%5Catop+%7B3x-y-5%3D0%7D%7D+%5Cright.+%5Cto+%5Cleft+%5C%7B+%7B%7By%3D1%7D+%5Catop+%7Bx%3D2%7D%7D+%5Cright.+)
![\left \{ {{y-1=0} \atop {x+2y-4=0}} \right. \to \left \{ {{y=1} \atop {x=2}} \right. \left \{ {{y-1=0} \atop {x+2y-4=0}} \right. \to \left \{ {{y=1} \atop {x=2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7By-1%3D0%7D+%5Catop+%7Bx%2B2y-4%3D0%7D%7D+%5Cright.+%5Cto+%5Cleft+%5C%7B+%7B%7By%3D1%7D+%5Catop+%7Bx%3D2%7D%7D+%5Cright.+)
Окончательный ответ:
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Также упростим первое уравнение
Получаем
Окончательный ответ:
karicha2000:
Большое спасибо :)
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