Question

Find two consecutive negative integers, sum of whose squares is 481.

Answer 1

Let the two consecutive negative integers be x and x + 1.

x² + (x + 1)² = 481

x² + x² + 2x + 1 = 481

2x² + 2x + 1 = 481

2x² + 2x + 1 − 481 = 0

2x² + 2x − 480 = 0

Both side divide by 2

x² + x − 240 = 0  

x² + 16x − 15x − 240 = 0  

x(x + 16) − 15(x + 16) = 0  

(x − 15)(x + 16) = 0

x − 15 = 0 or x + 16 = 0

x = 15 or x = −16

Since the integers are negative, choose x = −16.

x + 1

= −16 + 1

= −15

Hence, two consecutive negative integers are −16 and −15.