### Uzdevums:

10p.
Atrisini sistēmu:
$\left\{\begin{array}{l}{x}^{2}+{y}^{2}=13\\ \mathit{xy}=6\end{array}\right\$

Risinām kopā!
Papildini!
$\begin{array}{l}\underset{¯}{\left\{\begin{array}{l}{x}^{2}+{y}^{2}=13\\ 2\mathit{xy}=i\end{array}\right\\phantom{\rule{0.147em}{0ex}}|+}\\ \\ {\left(x+y\right)}^{2}=i\\ \\ \left|x+y\right|=i\end{array}$

Iegūst divas vienādojumu sistēmas
$\begin{array}{l}1\right)\left\{\begin{array}{l}x+y=i\\ \phantom{\rule{0.147em}{0ex}}\mathit{xy}=6\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\end{array}\right\\\ 2\right)\phantom{\rule{0.147em}{0ex}}\left\{\begin{array}{l}x+y=i\\ \mathit{xy}=6\end{array}\right\\end{array}$

Ar Vjeta teorēmu nosaki saknes!
Raksti atrisinājumus tā, lai $x$ vērtības ir dilstošā secībā (sāk ar lielāko)!
$\begin{array}{l}1\right)\left\{\begin{array}{l}x=i\\ y=i\end{array}\right\\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ 2\right)\left\{\begin{array}{l}x=i\\ y=i\end{array}\right\\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ 3\right)\phantom{\rule{0.147em}{0ex}}\left\{\begin{array}{l}x=i\\ y=i\end{array}\right\\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ 4\right)\left\{\begin{array}{l}x=i\\ y=i\end{array}\right\\end{array}$
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