Question

The sum of the squares of two consecutive natural number is 421 find the numbers

Answer 1

Answer:

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.