Correct option is C
Given:
We need integers
and such that:
9X² + 16Y² + 24 is a perfect square.
We want the smallest non-negative value of X + Y.
Solution: (smallest integer):
Try X = 0:
Expression = 16Y² + 24 → not a perfect square for any small Y ≥ 0.
(Checked: 24, 40, 88, 168, 280… none are perfect squares)
Try X = 1:
Expression = 9(1)² + 16Y² + 24
= 33 + 16Y²
Test small Y:
Y = 0 → 33 (not square)
Y = 1 → 33 + 16 = 49 = 7² → perfect square ✔
So (X, Y) = (1, 1) works.
Check if anything smaller exists:
(0,0), (1,0), (0,1)… all failed.
Thus this is the smallest pair.
Therefore:
X + Y = 1 + 1 = 2
Final Answer: 2
