The product of two natural numbers, one of which is 6 greater than the other, is 91. Find these numbers.

It is known from the condition that the product of two natural numbers, one of which is 6 more than the other, is equal to 91.

Let’s denote by variable x one of the numbers, then the second number can be written as (x + 6).

Let’s compose and solve the equation:

x (x + 6) = 91;

x * x + 6 * x – 91 = 0;

x ^ 2 + 6x – 91 = 0;

D = b ^ 2 – 4ac = 6 ^ 2 – 4 * 1 * (-91) = 36 + 364 = 400.

We are looking for roots by the formulas:

x1 = (-b + √D) / 2a = (-6 + 20) / 2 = 14/2 = 7;

x2 = (-b – √D) / 2a = (-6 – 20) / 2 = -26/2 = -13 – the number does not fit.

So, the first number is 7, and the second is 7 + 6 = 13.