The product of two natural numbers, one of which is 6 more than the other, is 187. Find these numbers.

Let x be one natural number, then (x + 6) is three times a natural number.

x * (x + 6) is the product of these numbers. By the condition of the problem, the product of the desired numbers is 187, which means that you can write the following equality: x * (x + 6) = 187.

Let’s solve the equation:

x * (x + 6) = 187,

x2 + 6x = 187,

x2 + 6x – 187 = 0.

By Vieta’s theorem, we can write that x1 * x2 = -6, x1 + x2 = -187, where x1 and x2 are the roots of the quadratic equation.

Using the selection method, we find that x1 = -17, x2 = 11.

x1 = -17 cannot be a solution to the problem, since -17 is not a natural number.

Hence, one natural number is 11. Calculate the second natural number:

x + 6 = 11 + 6 = 17.

Thus, the sought numbers are 11 and 17.