The sum of the squares of two consecutive odd natural numbers is 74. The sum of the numbers is:

Correct option is A

Given:

Sum of the squares of two consecutive odd natural numbers = 74

Solution:

$$x^2 + (x + 2)^2 = 74$$​

​$$x^2 + (x + 2)^2 = 74$$​

​$$x^2 + x^2 + 4x + 4 = 74$$​

​$$2x^2 + 4x + 4 = 74$$​​

​$$2x^2 + 4x - 70 = 0$$​

x$$^2 + 2x - 35 = 0$$​

x$$^2 + 2x - 35 = 0$$​

x$$^2 + 7x – 5x -35 = 0$$​

(x + 7)(x - 5) = 0

x = 5

x = -7

Take positive odd natural number: x = 5

Next number: x + 2 = 7

Sum = 5 + 7 = 12