Question

One number is 2 greater than another. The product of the numbers is 120. Find the numbers.One pair of the numbers, both of which are positive, is ___.​

Answer 1

The two positive numbers that satisfy the conditions of one being 2 greater than the other and their product being 120 are 10 and 12.

Step-by-step explanation:

The problem is to find two positive numbers where one number is 2 greater than another and their product is 120. Let's denote the smaller number as x. Therefore, the larger number would be x + 2. According to the problem, their product is x(x + 2) = 120.

Now we need to solve for x. Starting with the equation x(x + 2) = 120,

1. Expand the equation: x² + 2x = 120.
2. Bring all terms to one side to set the equation to zero: x² + 2x - 120 = 0.
3. Factor the quadratic equation: (x + 12)(x - 10) = 0.
4. Solving these factors gives x = -12 or x = 10. Since we are only interested in positive numbers, we discard x = -12.
5. Thus the smaller positive number is x = 10 and the larger number is x + 2 = 12.

So the two positive numbers that fit the requirements are 10 and 12.