Question

Решить систему уравнений ( 3x - y = 5 3x2 + y2 = 13

Answer 1

$\begin{cases}3x-y=5\\3x^2+y^2=13\end{cases}\Rightarrow\begin{cases}y=3x-5\\3x^2+(3x-5)^2=13\end{cases}\\3x^2+(3x-5)^2=13\\ 3x^2+9x^2-30x+25=13\\12x^2-30x+12=0\;\;\;\div6\\2x^2-5x+2=0\\D=25-4\cdot2\cdot2=9\\x_1=\frac12;\;x_2=2\\\begin{cases}y=3\cdot\frac12-5\\x=\frac12\end{cases}\quad\quad\quad\begin{cases}y=3\cdot2-5\\x=\frac12\end{cases}\\\begin{cases}y=-3\frac12\\x=2\end{cases}\quad\quad\quad\begin{cases}y=1\\x=2\end{cases}$