1 ) Эмм, условие неполное
2) положительное
3)не определить
4)бл, пиши нормально условия
5)нет
6)да
7)нет
У=-2х²+12
парабола, ветви вниз
координаты вершины (получим по формуле х₀=-b/(2a), так как b=0, то и х₀=0
6p/5xy+4k/3xy-3m/4x^2*2y; 6p/5xy+4k/3xy-3m/8x^2y; приводим к общему знаменателю 120x^2y → 144px+160kx-45m/120x^2y
![\left \{ {{x^2-3y^2=1} \atop {x-2y=1}} \right. \\ \\\left \{ {{(1+2y)^2-3y^2=1} \atop {x=1+2y}} \right. \\ \\\left \{ {{4y+y^2=0} \atop {x=1+2y}} \right. \\ \\\left \{ {{y(4+y)=0} \atop {x=1+2y}} \right. \\ \\\begin{cases} y=0\\y=-4\\x=1+2y \end{cases} \\ \\\begin{cases} y=0\\y=-4\\x=1+2*0\\x=1+2*(-4) \end{cases}\\ \\ \\\begin{cases} y=0\\y=-4\\x=1\\x=-7 \end{cases}](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%5E2-3y%5E2%3D1%7D%20%5Catop%20%7Bx-2y%3D1%7D%7D%20%5Cright.%20%5C%5C%20%5C%5C%5Cleft%20%5C%7B%20%7B%7B%281%2B2y%29%5E2-3y%5E2%3D1%7D%20%5Catop%20%7Bx%3D1%2B2y%7D%7D%20%5Cright.%20%5C%5C%20%5C%5C%5Cleft%20%5C%7B%20%7B%7B4y%2By%5E2%3D0%7D%20%5Catop%20%7Bx%3D1%2B2y%7D%7D%20%5Cright.%20%5C%5C%20%5C%5C%5Cleft%20%5C%7B%20%7B%7By%284%2By%29%3D0%7D%20%5Catop%20%7Bx%3D1%2B2y%7D%7D%20%5Cright.%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20y%3D0%5C%5Cy%3D-4%5C%5Cx%3D1%2B2y%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20y%3D0%5C%5Cy%3D-4%5C%5Cx%3D1%2B2%2A0%5C%5Cx%3D1%2B2%2A%28-4%29%20%5Cend%7Bcases%7D%5C%5C%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20y%3D0%5C%5Cy%3D-4%5C%5Cx%3D1%5C%5Cx%3D-7%20%5Cend%7Bcases%7D)
Ответ: (x=-7 y=-4) (x=1 y=0)
![\begin{cases} x^2+3xy-3y^2=1\\2x^2-xy+x^2=2 \end{cases} \\ \\\begin{cases} x^2+3xy-3y^2=1\\6x^2-3xy+3y^2=6 \end{cases} \\ \\\begin{cases} x^2+3xy-3y^2=1\\7x^2=7 \end{cases} \\ \\\begin{cases} x^2+3xy-3y^2=1\\x=1\\x=-1 \end{cases} \\ \\\begin{cases} 1+3y-3y^2=1\\1-3y-3y^2=1\\x=1\\x=-1 \end{cases} \\ \\\begin{cases} 3y-3y^2=0\\-3y-3y^2=0\\x=1\\x=-1 \end{cases} \\ \\\begin{cases} y(3-3y)=0\\-y(3+3y)=0\\x=1\\x=-1 \end{cases} \\ \\\begin{cases} y=1\\y=-1\\y=0\\x=1\\x=-1 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20x%5E2%2B3xy-3y%5E2%3D1%5C%5C2x%5E2-xy%2Bx%5E2%3D2%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20x%5E2%2B3xy-3y%5E2%3D1%5C%5C6x%5E2-3xy%2B3y%5E2%3D6%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20x%5E2%2B3xy-3y%5E2%3D1%5C%5C7x%5E2%3D7%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20x%5E2%2B3xy-3y%5E2%3D1%5C%5Cx%3D1%5C%5Cx%3D-1%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%201%2B3y-3y%5E2%3D1%5C%5C1-3y-3y%5E2%3D1%5C%5Cx%3D1%5C%5Cx%3D-1%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%203y-3y%5E2%3D0%5C%5C-3y-3y%5E2%3D0%5C%5Cx%3D1%5C%5Cx%3D-1%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20y%283-3y%29%3D0%5C%5C-y%283%2B3y%29%3D0%5C%5Cx%3D1%5C%5Cx%3D-1%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%5Cbegin%7Bcases%7D%20y%3D1%5C%5Cy%3D-1%5C%5Cy%3D0%5C%5Cx%3D1%5C%5Cx%3D-1%20%5Cend%7Bcases%7D)
Ответ: (x=-1 y=-1) (x=-1 y=0) (x=1 y=0) (x=1 y=1)