Question

Решите способом алгебраического сложения систему уравнений :

Answer 1

$\left\{\begin{array}{l}x^2+xy-6y^2=0\\x^2-5xy+2y^2+4=0\end{array}\right\ \ominus \ \left\{\begin{array}{l}x^2+xy-6y^2=0\ |:y^2\ne 0\\6xy-8y^2-4=0\end{array}\right\ \ \ ,\ \ t=\dfrac{x}{y}\\\\\\\left\{\begin{array}{l}t^2+t-6=0\\6xy-8y^2=4\end{array}\right\ \ \left\{\begin{array}{l}t_1=-3\ ,\ t_2=2\\6xy-8y^2=4\end{array}\right$

$a)\ \ \dfrac{x}{y}=-3\ \ ,\ \ x=-3y\ \ \to \ \ 6\cdot (-3y)\cdot y-8y^2=4\ ,\ \ -26y^2=4\ ,\\\\y^2=-\dfrac{2}{13}<0\ \ \ \Rightarrow \ \ y\in \varnothing \ ,\ tak\ kak\ \ y^2\geq 0\\\\b)\ \ \dfrac{x}{y}=2\ \ ,\ \ \ x=2y\ \ \to \ \ 6\cdot 2y\cdot y-8y^2=4\ \ ,\ \ 4y^2=4\ ,\ \ y^2=1\ \ \to \\\\y_1=-1\ \ ili\ \ y_2=1\\\\x_1=-2\ \ ili\ \ y_2=2\\\\Otvet:\ \ (-2;-1)\ ,\ (2;1)\ .$