Question

The sum of the squares of two consecutive natural numbers is 113.Find the numbers.

Answer 1

Question:-

The sum of the squares of two consecutive natural numbers is 113.Find the numbers.

Answer :-

Let the two consecutive natural numbers be x and x + 1

As per the given condition,

x2 + (x + 1)2 = 113

∴ x2 + x2 + 2x + 1 = 113

∴ 2x2 + 2x + 1 – 113 = 0

∴ 2x2 + 2x – 112 = 0

Dividing by 2 we get,

x2 + x – 56 = 0

∴ x2 + 8x – 7x – 56 = 0

∴ x (x + 8) – 7 (x + 8) = 0

∴ (x + 8) (x – 7) = 0

∴ x + 8 = 0 or x – 7 = 0

∴ x = – 8 or x = 7

∵ x is a natural number

∴ x cannot be negative

∴ x = 7

And x + 1 = 7 + 1 = 8

hope it helps you..

mark me as brainlist..

Answer 2

Let the numbers be n and n+1

then,

n²+(n+1)²=113²

n² +2n−112=0

n²+n−56=0

n²+8n−7n−56=0

(n+8)(n−7)=0

n=7,−8

Neglect the negative value.

Numbers are 7 and 8.