let 'x' be the first number
let 'y' be the second number
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their product is 1872
x (y) = 1872 -----equation 1
their sum is 88
x + y = 88 -----equation 2
- - - - - - -
from equation 2
x + y = 88
x = 88 - y -------equation 2'
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substitute equation 2' to equation 1
x (y) = 1872
(88-y) (y) = 1872
88y -y^2 = 1872
transpose 88y -y^2 to the right
0 = y^2 -88y + 1872
or
y^2 -88y + 1872 = 0
factor
(y-36)(y-52) = 0
y-36=0
y=36
y-52=0
y=52
if y=36
x = 88 -y
x = 88 -36
x = 52
if y = 52
x = 88 - y
x = 88 - 52
x = 36
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their difference would be
52 - 36 = 16
