Question

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Answer 1

Let one of the number be x then the other number be x + 2.

Then according to question,

$$\begin{gathered} x^2+{\left(x+2\right)}^2=394 \\ \Rightarrow x^2+x^2+4x+4=394 \\ \Rightarrow 2x^2+4x-390=0 \\ \Rightarrow x^2+2x-195=0 \\ \Rightarrow x^2+15x-13x-195=0 \\ \Rightarrow x(x+15)-13(x+15)=0 \\ \Rightarrow (x-13)(x+15)=0 \\ \Rightarrow x-13=0\mathrm{or}x+15=0 \\ \Rightarrow x=13\mathrm{or}x=-15 \end{gathered}$$

Since, x being an odd number,

Therefore, x = 13.

Then another number will be

$x+2=13+2=15$

Thus, the two consecutive odd numbers are 13 and 15.