Question

Find the two natural numbers which differ by 5 and the sum of whose squares is 97.

Answer 1

Let the two numbers be x and x + 5.

From the given information,

x² + (x + 5)² = 97

2x² + 10x + 25 – 97 = 0

2x² + 10x – 72 = 0

x² + 5x – 36 = 0

(x + 9)(x – 4) = 0

x = –9 or 4

Since, –9 is not a natural number.

So, x = 4.

Thus, the numbers are 4 and 9.