[tex]\begin{cases} x+y=129 \\xy=3348 \end{cases}\\\\ \begin{cases} y =129-x \\xy=3348 \end{cases}\\ \\ substitution : \\ (129-x)x=3348\\\\129x-x^2=3348[/tex]
[tex]129x-x^2=3348 \\ \\x^2-129x+3348 =0 \\ \\ x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{129-\sqrt{ (-129)^2-4 \cdot1 \cdot3348 }}{2 }= \frac{129-\sqrt{ 16641-13392 }}{2 }=\\\\=\frac{129-\sqrt{ 3249 }}{2 }= \frac{129-57}{2 }= \frac{72 }{2 }= 36 \\ \\[/tex]
[tex]x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{129+\sqrt{ (-129)^2-4 \cdot1 \cdot3348 }}{2 }= \frac{129+57}{2 }= \frac{186 }{2 }= 93 \\ \\ \begin{cases}y=129-x \\ x=36 \end{cases} \ \ \ or \ \ \ \begin{cases}y=129-x \\ x=93 \end{cases}\\\\ \begin{cases}y=129-36 \\ x=36 \end{cases} \ \ \ or \ \ \ \begin{cases}y=129-93 \\ x=93 \end{cases}\\\\ \begin{cases}y=93 \\ x=36 \end{cases} \ \ \ or \ \ \ \begin{cases}y=36 \\ x=93 \end{cases}[/tex]
