let x = first number
y = second number
(1) xy = 1800
(2) x + y = 105
y = 105 - x
we will substitute y to the first equation
(1) (x)(105 - x) = 1800
[tex]105x - x^2 - 1800 = 0
[/tex]
[tex]x^2 - 105x + 1800 = 0
[/tex]
Using formula [tex] \frac{-b+ \sqrt{ b^{2} -4ac} }{2a} [/tex]
a = 1, b = -105, c = 1800
[tex] \frac{-(-105)+ \sqrt{ (-105)^{2}- 4(1)(1800) } }{2(1)} [/tex] = x
[tex] \frac{105+ \sqrt{11025-7200} }{2} =x[/tex]
[tex] \frac{105+61.85}{2} = x
[/tex]
[tex] \frac{166.85}{2} =x[/tex]
[tex]x=83.43[/tex]
(2) x + y = 105
we'll substitute x = 83.43
83.43 + y = 105
y = 105 - 83.43
y = 21.57
Therefore, the two numbers are 83.43 and 21.57
