Question

Find two consecutive odd integers such that the square of the larger is one less than twice the square of the smaller.

Answer 1

5 and 7

Check -- do those numbers work?

Answer 2

(n+2)^2 = 2n^2 - 1

You might think that it would be possible for n to be even, but since the right side must be odd, so must n^2 be odd, and thus any solutions you find will be odd.

Answer 3

Find two consecutive even integers such that the sum of the larger and twice the smaller is 124.