Correct Answer: 255

Solution :
Let the three numbers be a, b and c.
According to the question,
a ² + b ² + c ² = 323 and a ² + b ² = 2c
⇒ c ² + 2c = 323
⇒ c ² + 2c – 323 = 0
⇒ (c + 19) (c – 17) = 0
Taking, c = 17 as c can't be negative.
⇒ a ² + b ² = 2c
⇒ a ² + b ² = 2 × 17
⇒ a ² + b ² = 34
⇒ a ² + b ² = 25 + 9
⇒ a ² + b ² = 5 ² + 3 ²
Comparing both sides we get, a = 5 and b = 3 (taking a > b)
So, the product of a, b, and c = 3 × 5 × 17 = 255
Hence, the correct answer is 255.