Question

The sum of the squares of two consecutive natural numbers is 41. Find the numbers.

Answer 1

Let the numbers be x and x + 1.

From the given information,

x² + (x + 1)² = 41

2x² + 2x + 1 – 41 = 0

x² + x – 20 = 0

(x + 5)(x – 4) = 0

x = –5, 4

But, –5 is not a natural number.

So, x = 4.

Thus, the numbers are 4 and 5.