Answer 1

Let the consecutive odd positive integers are 2x – 1 and 2x + 1

Given that the sum of the squares is 394.

⇒ (2𝑥 - 1)² + (2𝑥 + 1)2 = 394

⇒ 4𝑥² + 1 - 4𝑥 + 4𝑥² + 1 + 4𝑥 = 394

⇒ 8𝑥² + 2 = 394

⇒ 4𝑥² = 392

⇒ 𝑥² = 36

⇒ x = 6

As x = 6, 2x - 1 = 2 × 6 - 1 = 11

2x + 1 = 2 × 6 + 1 = 13

∴ The two consecutive odd positive numbers are 11 and 13.