One number is equal to the square of another. find the numbers if both are positive and their sum is 4242.

Let one number be x.
The other number is x².

Find x:

x² + x = 42
x² + x - 42 = 0
(x + 7) (x - 6) = 0
x = - 7 or x = 6

x = -7 is rejected since the question asked for a positive number.

Find the numbers:
one number = x = 6
the other number =6² = 36

6 and 36