Question

the sum of the squares of two consecutive odd natural number is greater than 8 times their by 2.find the numbers

Answer 1

➡HERE IS YOUR ANSWER⬇

Let, the consecutive odd numbers are (2n+1) and (2n+3), where n belongs to the set of integers.

Given that :

(2n+1)² + (2n+3)² = 8{(2n+1)+(2n+3)} + 2

or, (4n²+4n+1) + (4n²+12n+9) = 8(4n+4) + 2

or, 8n²+16n+10 = 32n+34

or, 8n²-16n-24 = 0

or, n²-2n-3 = 0

or, (n-3)(n+1)

So, n = 3 and n = -1.

But, the question mentions of Natural numbers. So we take n = 3.

Therefore, the numbers are

7 and 9.

⬆HOPE THIS HELPS YOU⬅

Answer 2

the explanation is above.

the answer will be 7 and 9