Question

Find two consecutive positive integers ,sum of whose squares is 1405​

Answer 1

Answer:

the numbers are 26 and 27

Step-by-step explanation:

let the numbers be x and x+1. then,

x² + (x+1)² = 1405

x² + x² +2x +1 = 1405

2x² + 2x = 1404

x² +x = 702

x² + x + (½)² = 702 + ¼

(x +½)² = 2809/4

x +½ = 53/2

x = 53/2 - 1/2

= 52/2

= 26.

26² + 27² = 676 + 729

= 1405