Question

3) Solve any one subquestion of the following.
3
1) The sum of squares of two consecutive even natural
number is 244. Find the numbers.​

Answer 1

Answer:

let 2 consecutive even natural number be 2n and 2n+2

Given that

(2n)^2 + (2n+2)^2 = 244

4n^2 + 4n^2 + 4 + 8n = 244

8n^2 + 8n + 4 = 244

2n^2 + 2n +1 = 61

2n^2 + 2n - 60 = 0

solving the quadratic equation

n^2 + n - 30 = 0

n^2+6n-5n-30=0

n(n+6)-5(n+6)=0

(n+6)(n-5)=0

n= -6 or n = 5

since n is a natural number

n=5

1st number = 2n =2×5=10

2nd number = 2n+2=10+2=12