Question

Rezolvati sistemul de la problema S:E20.182. Multumesc!

Answer 1

$\begin{cases}(x + y - 3) {}^{2019}\cdot5 {}^{2020} + 5(x - y) = 5 \\ (x + y - 3) {}^{2019}\cdot125 {}^{673} - 2(x - y) = - 2 \end{cases} \\ \\ \begin{cases}5 [(x + y - 3) {}^{2019}\cdot5 {}^{2019} + x - y ] = 5 \\ (x + y - 3) {}^{2019}\cdot5 {}^{2019} - 2x + 2y = - 2 \end{cases} \\ \\ \begin{cases}(x + y - 3) {}^{2019}\cdot5 {}^{2019} + x - y = 1 \\ (5x + 5y - 15) {}^{2019} - 2x + 2y = - 2 \end{cases} \\ \\ \begin{cases}(5x + 5y - 15) {}^{2019} + x - y = 1 \\ (5x + 5y - 15) {}^{2019} - 2x + 2y = - 2 \end{cases} \\ \\ \begin{cases} - [ (5x + 5y - 15) {}^{2019} ] - x + y = - 1 \\ (5x + 5y - 15) {}^{2019} - 2x + 2y = - 2 \end{cases} \\ \\ \begin{cases} - x + y = - 1 \\ - 2(x - y) = - 2\end{cases} \\ \\ \begin{cases} - x + y = - 1 \\ x - y = 1\end{cases} \\ \\ x = 1 + y \\ \implies \: - 2(1 + y - y) = - 2 \\ \\ \implies \: y\in\mathbb{R} \\ \implies \: x = 1 + y$

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