Question

Find two consecutive positive odd numbers, the sum of whose squares is 74.

Answer 1

Let the consecutive positive odd numbers be x and x + 2.

From the given information,

x² + (x + 2)² = 74

2x² + 4x + 4 = 74

2x² + 4x – 70 = 0

x² + 2x – 35 = 0

(x + 7)(x – 5) = 0

x = –7, 5

Since, the numbers are positive, so, x = 5.

Thus, the numbers are 5 and 7.