Find three consecutive integers odd integers such that the square of the first increased by twice the second is equal to two less than three times the third

Answer 1

If the smallest is x, then
x^2 + 2(x+2) = 3(x+4)-2
Unfortunately, this will not work (why?)
To make sure x is odd, we need x = 2k+1
Then we solve
(2k+1)^2 + 2(2k+3) = 3(2k+5)-2