Question

3) [x² - y² = -8, 2 xy = 3; dam 100 balow​ с решением на фото

Answer 1

Ответ:

$(-1;-3);\ (1;3)$

Объяснение:

$x,y \neq 0$

$\begin{cases}x^2-y^2=-8\\xy=3\end{cases}$

$\begin{cases}x^2-y^2=-8\\y=\frac{3}{x}\end{cases}$

$\begin{cases}x^2- \left(\frac{3}{x}\right)^2=-8\\y=\frac{3}{x}\end{cases}$

$x^2- \left(\frac{3}{x}\right)^2=-8$

$x^2-\frac{9}{x^2}=-8$

$\frac{x^4}{x^2}-\frac{9}{x^2}+\frac{8x^2}{x^2}=0$

$\frac{x^4-9+8x^2}{x^2}=0$

$x^4+8x^2-9=0$

подставляем

$x^2=t, t > 0\\\\t^2+8t-9=0\\\\t^2+9t-t-9=0\\\\t(t+9)-(t+9)=0\\\\(t+9)(t-1)=0\\\\t+9=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ t-1=0\\\\t=-9 < 0\ \ \ \ \ \ \ \ \ \ \ \ t=1$

$x^2=1\\\\x^2-1=0\\\\(x-1)(x+1)=0\\\\x-1=0\ \ \ \ \ \ \ \ \ \ x+1=0\\\\x=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-1$

$\begin{cases}x=1\\y=\frac{3}{x}\end{cases}\\\\\begin{cases}x=1\\y=\frac{3}{1}\end{cases}\\\\\begin{cases}x=1\\y=3\end{cases}$                                           $\begin{cases}x=-1\\y=\frac{3}{x}\end{cases}\\\\\begin{cases}x=-1\\y=\frac{3}{-1}\end{cases}\\\\\begin{cases}x=-1\\y=-3\end{cases}$