1) (x^2 + 3y)^2 = x^4 + 6x^2y + 9y^2
2) ( 0,2m^2 - 5n)^2 = 0,04m^4 - 2m^2n + 25n^2
Х ведро керосина
х+2 ведро воды
4(х+2)=5х
4х+8=5
х=8кг масса ведра керосина
X(x-22)+14=0
x²-22x+14=0
D=(-22)²-4*1*14=484 - 56 = 428
<u>x₁=</u> (22 + √428) / 2 = <u>(22 + 2√107) / 2</u>
<u>x₂= </u>(22 - √428) / 2 =<u> (22 - 2√107) /2</u>
![\left\{{{x^2-y^2=-5}\atop{x^2+y^2=13}}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%7B%7Bx%5E2-y%5E2%3D-5%7D%5Catop%7Bx%5E2%2By%5E2%3D13%7D%7D%5Cright.)
Сложим эти уравнения:
![x^2-y^2+x^2+y^2=-5+13](https://tex.z-dn.net/?f=x%5E2-y%5E2%2Bx%5E2%2By%5E2%3D-5%2B13)
![x^2+x^2=-5+13](https://tex.z-dn.net/?f=x%5E2%2Bx%5E2%3D-5%2B13)
![2x^2=8](https://tex.z-dn.net/?f=2x%5E2%3D8)
![x^2=8:2](https://tex.z-dn.net/?f=x%5E2%3D8%3A2)
![x^2=4](https://tex.z-dn.net/?f=x%5E2%3D4)
![x_1=-\sqrt{4}=-2](https://tex.z-dn.net/?f=x_1%3D-%5Csqrt%7B4%7D%3D-2)
![x_2=\sqrt{4}=2](https://tex.z-dn.net/?f=x_2%3D%5Csqrt%7B4%7D%3D2)
Подставим значение х вo второе уравнение ![x^2+y^2=13.](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D13.)
![1)x_1=-2;=>(-2)^2+y^2=13;=>y^2=13-4](https://tex.z-dn.net/?f=1%29x_1%3D-2%3B%3D%3E%28-2%29%5E2%2By%5E2%3D13%3B%3D%3Ey%5E2%3D13-4)
![y^2=9](https://tex.z-dn.net/?f=y%5E2%3D9)
![y_1=-\sqrt{9}=-3](https://tex.z-dn.net/?f=y_1%3D-%5Csqrt%7B9%7D%3D-3)
![y_2=\sqrt{9}=3](https://tex.z-dn.net/?f=y_2%3D%5Csqrt%7B9%7D%3D3)
![2)x_2=2;=>2^2+y^2=13;=>y^2=13-4](https://tex.z-dn.net/?f=2%29x_2%3D2%3B%3D%3E2%5E2%2By%5E2%3D13%3B%3D%3Ey%5E2%3D13-4)
![y^2=9](https://tex.z-dn.net/?f=y%5E2%3D9)
![y_3=-\sqrt{9}=-3](https://tex.z-dn.net/?f=y_3%3D-%5Csqrt%7B9%7D%3D-3)
![y_4=\sqrt{9}=3](https://tex.z-dn.net/?f=y_4%3D%5Csqrt%7B9%7D%3D3)
Ответ: (-2; -3); (-2; 3); (2; -3); (2; 3).
Ну вроде так xy+3x-2y=9
xy(3-2)=9
xy=9