Question

Which equation supports the given conjecture? i will give medals

The sum of the squares of two consecutive integers is an odd integer.

A.
(2 + 3)2

B.
32 + 52 = 34

C.
4 + 52 = 29

D.
52 + 62 = 61

Answer 1

I'd start with an algebraic approach: I'd let x be the first integer and (x+1) be the second.
Squaring each of these quantities separately, we get

x^2 + (x+1)^2 = some odd integer.

Supposing that x=2, then x+1 =3 would be the next consecutive integer. Squaring x and x+1, or squaring 2 and 3, results in 2^2 and 3^2, or 4 and 9, whose sum is 13 (an odd integer). This is not the final answer, but rather an illustration of what is meant by "The sum of the squares of two consecutive integers is an odd integer."

How we'd get from there to one of the four possible answers, I don't know. I do see that the quantity "The sum of the squares of two consecutive integers" does not appear in any of the choices: 32, 52, 62, and so on.

Are you completely sure that you've copied the problem down correctly?

Answer 2

The four answer choices are

(2 + 3)2

B.
32 + 52 = 34

C.
4 + 52 = 29

D.
52 + 62 = 61

Please note that the first one is not an equation, and that the remaining four, while equations, are all false. for example: 4+52=56 (not 29).