Find three consecutive natural numbers if you know that the square of the larger of them is 37

Find three consecutive natural numbers if you know that the square of the larger of them is 37 more than the product of two other numbers.

Let’s denote the least of the required numbers through x, then the other two will be equal to x + 1 and x + 2.
We compose an equation according to the condition of the problem
(x + 2) ^ 2 = x * (x + 1) +37
We open the brackets in about both sides of the equation and solve it
x ^ 2 + 4x + 4 = x ^ 2 + x +37
4x + 4 = x + 37
4x – x = 37 -4
3x = 33
x = 11
Thus, the required numbers
x = 11
x + 1 = 12
x + 2 = 13

Examination
13 ^ 2 = 11 * 12 +37
169 = 132 +37

Answer: 11,12,13