3((2а)^2+4ав+(в)^2)-10ав
3(4а^2+4ав+в^2)-10ав
12а^2+4ав+3в^2-10ав
15а^2-6ав.
15*12-6*корень(12)*корень(3)
180-36=144
![1.\;\begin{cases}2\sin2x+tg3y=2\\6\sin2x-2tg3y=1\end{cases}](https://tex.z-dn.net/?f=1.%5C%3B%5Cbegin%7Bcases%7D2%5Csin2x%2Btg3y%3D2%5C%5C6%5Csin2x-2tg3y%3D1%5Cend%7Bcases%7D)
Прибавим ко второму уравнению удвоенное первое.
![\begin{cases}2\sin2x+tg3y=2\\8\sin2x=5\end{cases}\Rightarrow\begin{cases}\frac54+tg3y=2\\\sin2x=\frac58\end{cases}\Rightarrow\begin{cases}tg3y=\frac34\\\sin2x=\frac58\end{cases}\Rightarrow\\\Rightarrow\begin{cases}3y=acrtg\left(\frac34\right)+\pi k\\2x=(-1)^n\cdot\arcsin\left(\frac58\right)+\pi n\end{cases}\Rightarrow\begin{cases}y=\frac13acrtg\left(\frac34\right)+\frac{\pi k}3\\x=\frac12\cdot(-1)^n\cdot\arcsin\left(\frac58\right)+\frac{\pi n}2\end{cases}\\n,\;k\in\mathbb{Z}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D2%5Csin2x%2Btg3y%3D2%5C%5C8%5Csin2x%3D5%5Cend%7Bcases%7D%5CRightarrow%5Cbegin%7Bcases%7D%5Cfrac54%2Btg3y%3D2%5C%5C%5Csin2x%3D%5Cfrac58%5Cend%7Bcases%7D%5CRightarrow%5Cbegin%7Bcases%7Dtg3y%3D%5Cfrac34%5C%5C%5Csin2x%3D%5Cfrac58%5Cend%7Bcases%7D%5CRightarrow%5C%5C%5CRightarrow%5Cbegin%7Bcases%7D3y%3Dacrtg%5Cleft%28%5Cfrac34%5Cright%29%2B%5Cpi+k%5C%5C2x%3D%28-1%29%5En%5Ccdot%5Carcsin%5Cleft%28%5Cfrac58%5Cright%29%2B%5Cpi+n%5Cend%7Bcases%7D%5CRightarrow%5Cbegin%7Bcases%7Dy%3D%5Cfrac13acrtg%5Cleft%28%5Cfrac34%5Cright%29%2B%5Cfrac%7B%5Cpi+k%7D3%5C%5Cx%3D%5Cfrac12%5Ccdot%28-1%29%5En%5Ccdot%5Carcsin%5Cleft%28%5Cfrac58%5Cright%29%2B%5Cfrac%7B%5Cpi+n%7D2%5Cend%7Bcases%7D%5C%5Cn%2C%5C%3Bk%5Cin%5Cmathbb%7BZ%7D)
![2.\;\begin{cases}2x+3y=1\\4x+6y=5\end{cases}](https://tex.z-dn.net/?f=2.%5C%3B%5Cbegin%7Bcases%7D2x%2B3y%3D1%5C%5C4x%2B6y%3D5%5Cend%7Bcases%7D)
Разделим второе уравнение на 2.
![\begin{cases}2x+3y=1\\2x+3y=2,5\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D2x%2B3y%3D1%5C%5C2x%2B3y%3D2%2C5%5Cend%7Bcases%7D)
Данная система не имеет решений, т.к. её уравнения противоречат друг другу.