Κυριακή 23 Μαρτίου 2025

Επτά Συμμετρικά Συστήματα

Να λυθούν τα συστήματα:
\[ 1.\begin{cases} x + 2y + z = 14 \\ 2x + y + z = 12 \\ x + y + 2z = 18 \end{cases}\] \[2. \begin{cases} x + y = 7 \\ y + z = -2 \\ z + x = 9 \end{cases} \]
\[3. \begin{cases} xy = 6 \\ yz = -2 \\ zx = 10 \end{cases} \] \[ 4.\begin{cases} (x+1)(y+1) = 24 \\ (y+1)(z+1) = 30 \\ (z+1)(x+1) = 20 \end{cases} \] \[ 5.\begin{cases} xy - x - y = 11 \\ yz - y - z = 14 \\ zx - x - z = 19 \end{cases} \] \[ 6.\begin{cases} x(x+y+z) = 4 \\ y(x+y+z) = 6 \\ z(x+y+z) = 54 \end{cases} \] \[ 7.\begin{cases} x + [y] + [z] = 1.1 \\ [x] + y + [z] = 2.2 \\ [x] + [y] + z = 3.3 \end{cases} \]

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