Answer:
21, 7
Step-by-step explanation:
1st number = x, 2nd number = y
Given x + 3y = 42 (1)
find maximum value of xy.
Multiply by x on (1), get
x^2 + 3xy = 42x
3xy = -x^2 + 42x = -(x^2 - 42x)
Make a perfect square,
3xy = -(x^2 - 42x + 21^2) + 21^2
3xy = 21^2 - (x - 21)^2
Note (x - 21)^2 is non-negative, so when x = 21, the right hand side has a maximum value of 21^2, so xy is a maximum.
Use (1) and x = 21, we get 21 + 3y = 42, 3y = 21, y = 7
Hence, the two positive real numbers are 21 and 7
