Question

prove that the sum of two continues odd number is multiple of 4​

Answer 1

Answer:

Let the 2 consecutive odd Numbers be 2n-1 and 2n+1.

Squaring both the Numbers and adding them, we get:

4n^2 - 4n + 1 + 4n^2 + 4n + 1

This is nothing but 8n^2 + 2.

With this, we can clearly see that the final Number (8n^2 + 2) is just a multiple of 2 but definitely not a multiple of 4. This is because we can take 2 common and we get

2(4n^2 + 1). Now 4n^2 is an even Number (since we are multiplying n^2 by 4) and adding one to it to get an odd Number. In other words, we are getting a final Number that’s some odd number multiplied by 2.

Thus we can see that the final Number that we get is divisible by 2 but not by 4.

Step-by-step explanation:

How can you prove that the sum of the squares of two consecutive odd numbers will not be a multiple of 4?

How can you prove that the sum of the squares of two consecutive odd numbers will not be a multiple of 4?Let’s choose an arbitrary odd number n .