SOLUTION: The difference of two numbers is 8; the product is 65. Find the numbers.

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The difference of two numbers is 8;
x - y = 8
x = (y+8)
:
the product is 65.
x*y = 65
:
replace x with (y+8)
y(y+8) = 65
:
y^2 + 8x - 65 = 0
Factor
(y+13)(y-5) = 65
Two solutions
y = -13; then x = -13 + 8 = -5
y = +5; then x = 5 + 8 = +13