Step-by-step explanation:
Let the two numbers be x and y.
[tex] \therefore \: xy = - 8...(1) \\ and \\ x + y = 2 \\ \\ \therefore \:x = 2 - y...(2)[/tex]
From equations (1) & (2)
[tex] (2-y)y=-8\\
\therefore \: 2y - y^2 = - 8\\\\
\therefore \:y^2 - 2y-8=0\\\\
\therefore \:y^2 - 4y+2y-8=0\\\\
\therefore \:y(y - 4)+2(y-4)=0\\\\
\therefore \:(y+2)(y - 4)=0\\\\
\therefore \:(y+2)=0\:\: or\:\:(y - 4)=0\\\\
\therefore \:y=-2\:\: or\:\:y =4\\\\
When \:\: y = - 2\implies x = 4\\\\
When \:\: y = 4\implies x = - 2\\
[/tex]
Thus, the two numbers are (4, - 2) or (-2, 4).
