Question

Three consecutive odd natural numbers are such that the product of the first and third is greater than four times
the middle by 1. Find the numbers.

Answer 1

Let the three consecutive odd natural numbers be x, (x + 2) and (x + 4). Then, by the given condition, we have:
x(x + 4) = 4(x + 2) + 1
$\Rightarrow$ x² + 4x = 4x + 8 + 1
$\Rightarrow$ x² = 9
$\Rightarrow$ x = ± 3
Since x is an odd natural number, x = 3, x + 2 = 3 + 2 = 5 and x + 4 = 3 + 4 = 7
Thus, the three consecutive odd natural numbers are 3, 5, 7.