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Résoudre \[S_1\left\{\begin{array}{rcrcrcl} x&+&\cosh a\ y&+&\cosh 2a\ z&=&\cosh 3a\\[3pt] \cosh a\ x&+&\cosh 2a\ y&+&\cosh 3a\ z&=&\cosh 4a\\[3pt] \cosh 2a\ x&+&\cosh 3a\ y&+&\cosh 4a\ z&=&\cosh 5a\end{array}\right.\] et \[S_2 \left\{\begin{array}{rcrcrcrcl} x_1&+&x_2&+&\ldots&+&x_n&=&1\\[3pt] x_1&+&2x_2&+&\ldots&+&nx_n&=&0\\[3pt] x_1&+&2^2x_2&+&\ldots&+&n^2x_n&=&0\\[3pt] & & & &\vdots& & & & \\[3pt] x_1&+&2^{n-1}x_2&+&\ldots&+&n^{n-1}x_n&=&0\end{array}\right.\]