The product of two numbers is 48 and the sum of their reciprocal a is 1/3. Determine the value of the two numbers.
two numbers: x and y
xy = 48 ---> y = 48/x
and 1/x + 1/y = 1/3
(x+y)/(xy) = 1/3
(x+y)/48 = 1/3
x+y = 16
x + 48/x = 16
x^2 + 48 = 16x
x^2 - 16x + 48 = 0
(x-12)(x-4) = 0
x = 12 or x = 4
if x = 12, y = 48/12 = 4
if x = 4, y = 48/4 = 12
The two numbers are 12 and 4