let the two number be x and y
x + y = 156
y = 156 - x
Product of the 2 numbers:
x(156 - x) = [tex] 156x - x^{2} [/tex]
This maximum value occurs when x = -b / (2a). [This is a standard rule]
a = -1 and b = 156
x = [tex]x = \frac{-156}{-2} [/tex]
x = 78
y = 156 - 78 = 78
product = 78 x 78 = 6084
So the two positive numbers are 78 and 78.
