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
\(105x - x^2 - 1800 = 0\)
\(x^2 - 105x + 1800 = 0\)
Using formula \(\frac{-b+ \sqrt{ b^{2} -4ac} }{2a}\)
a = 1, b = -105, c = 1800
\(\frac{-(-105)+ \sqrt{ (-105)^{2}- 4(1)(1800) } }{2(1)}\) = x
\(\frac{105+ \sqrt{11025-7200} }{2} =x\)
\(\frac{105+61.85}{2} = x\)
\(\frac{166.85}{2} =x\)
\(x=83.43\)
(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
