Question

Prove that the sum of the squares of two odd integers cannot be a perfect square

Answer 1

➡HERE IS YOUR ANSWER⬇

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

Now,

${(2n + 1)}^{2} + {(2n + 3)}^{2} \\ \\ = (4 {n}^{2} + 4n + 1) + (4 {n}^{2} + 12n + 9) \\ \\ = 8 {n}^{2} + 16n + 10$

which is for sure not a perfect square for all values of n.

Hence, proved.

⬆HOPE THIS HELPS YOU⬅

Answer 2

Answer:

yeah I will obviously answer