Question

find two consecutive natural number of whose square are 481

Answer 1

hey dear
x² + (x + 1)² = 481 
x² + x² + x + x + 1 = 481 
2x² + 2x = 480 
x² + x = 240 
x² + 1/2x = 240 + (- 1/2)² 
x² + 1/2x = 960/4 + 1/4 
(x + 1/2)² = 961/4 
x + 1/2 = 31/2 
x = 30/2 or 15 

Greater integer: 
= 15 + 1 
= 16 ..
I hope it help's u

Answer 2

let the two consecutive natural numbers be x and (x + 1)
Given x^2+ (x + 1)^2= 421
x^2+ x^2+ 2x + 1 – 421 = 0
2x^2+ 2x – 420 = 0
x^2+ x – 210 = 0
x^2+ 15x – 14x – 210 = 0
(x + 15)(x – 14) = 0
Hence x = -15 or 14
Since x is a natural number
Thus x = 14
x + 1 = 15
Therefore the two consecutive numbers are 14 and 15.