The sum of the squares of two consecutive positive odd numbers is 394. What is the larger of the two numbers?

Explanation

1. 01

   Let them be $x$ and $x + 2$: $x^2 + (x + 2)^2 = 394$.

2. 02

   $2x^2 + 4x + 4 = 394$, so $x^2 + 2x - 195 = 0$.

3. 03

   $(x + 15)(x - 13) = 0$; positive root $x = 13$.

4. 04

   The numbers are 13 and 15; check $169 + 225 = 394$.