\(x-y-z+3=0\Leftrightarrow x=y+z-3\)
\(x^2-y^2-z^2=\left(y+z-3\right)^2-y^2-z^2=y^2+z^2+9+2yz-6y-6z-y^2-z^2\)
\(=2yz-6y-6z+9=1\)
\(\Leftrightarrow yz-3y-3z+4=0\)
\(\Leftrightarrow\left(y-3\right)\left(z-3\right)=5=1.5=\left(-1\right).\left(-5\right)\)
Xét bảng:
y-3 | 1 | 5 | -1 | -5 |
z-3 | 5 | 1 | -5 | -1 |
y | 4 | 8 | 2 | -2 |
z | 8 | 4 | -2 | 2 |
x | 9 | 9 | -3 | -3 |