Question

Find two consecutive positive integers such that the sum of their squares is 181.

Answer 1

Given:

Find two consecutive positive integers such that the sum of their squares is 181.

Let the smaller integer be x.

Then the next consecutive integer is x + 1.

x² and (x + 1)²

x² + (x + 1)² = 181

x² + (x² + 2x + 1) = 181

x² + x² + 2x + 1 = 181

Subtract 181 from both sides:

2x² + 2x + 1 − 181 = 0

2x² + 2x − 180 = 0

Divide the whole equation by 2:

x² + x − 90 = 0

Find factors of −90 that add to +1:

10 × (−9)

= −90 and

10 + (−9) 

= 1

(x + 10) (x − 9) = 0

x = −10 or x = 9

Since we want positive integers, take:

x = 9, x + 1 = 10

9 and 10​