Question

это система
X^2 - y^2 = 12
2x^2 + 2xy = 48

^2 это квадрат

Answer 1

Ответ:

$\left\{\begin{array}{l}x^2-y^2=12\\2x^2+2xy=48\end{array}\right\ \ \left\{\begin{array}{l}(x-y)(x+y)=12\\2x(x+y)=48\end{array}\right\ \ \left\{\begin{array}{l}x+y=\dfrac{12}{x-y}\\x+y=\dfrac{24}{x}\end{array}\right\\\\\\\dfrac{12}{x-y}=\dfrac{24}{x}\ \ ,\ \ \ \dfrac{1}{x-y}=\dfrac{2}{x}\ \ ,\ \ \ x=2(x-y)\ \ ,\ \ x=2x-2y\ \,\ \ \underline {\ x=2y\ }\\\\\\x^2-y^2=(2y)^2-y^2=3y^2\ \ ,\ \ 3y^2=12\ \ ,\ \ y^2=4\ \ ,\ \ \underline{\ y=\pm 2\ }\\\\\\a)\ \ y=-2\ \ \to \ \ x=2y=2\cdot (-2)=-4$

$b)\ \ y=2\ \ \to \ \ \ x=2y=2\cdot 2=4\\\\\\Otvet:\ \ (-4\, ;-2\, )\ ,\ (\ 4\ ;\ 2\ )\ .$