If a and b are positive integers and a^2 - b^2 = 21, what is the value of a^2 + b^2?
Correct: C
We can factor a^2 - b^2 as (a + b)(a - b) = 21. Since a and b are positive integers, the possible pairs of factors of 21 are (21, 1) and (7, 3). If (a + b, a - b) = (21, 1), then adding the equations gives 2a = 22, so a = 11. Then b = 10. If (a + b, a - b) = (7, 3), then adding the equations gives 2a = 10, so a = 5. Then b = 2. Since the problem does not specify which value to use, let's proceed with a=5 and b=2. Then a^2 + b^2 = 5^2 + 2^2 = 25 + 4 = 29.