Question

Prove that the sum of any positive integer and its square is an even number.​

Answer 1

Answer

The sum of an integer x and its square is x2 + x. Now, since x is either even or odd, there is some integer k such that either x = 2k if x is even or x = (2k + 1) if x is odd. If x = 2k, then x2 + x = (2k)2 + 2k, which equals 4k2 + 2k, which by factoring equals 2(2k2 + k), which is even. On the other hand, if x = (2k + 1), then x2 + x = (2k + 1)2 + (2k + 1), which equals 4k2 + 4k + 1 + 2k + 1, which equals 4k2 + 6k + 2, which by factoring equals 2(2k2 + 3k + 1), which is also even.

Answer 2

Answer:

Square or sum of any positive numbers is not always even.

Step-by-step explanation:

2+2=4

but,

3*3=9,3+2=5.