The difference of two numbers is 1. The product of the two numbers is 6. What are the two numbers?

Let's denote the two numbers as x and y.

From the problem, we have two equations:

1. x - y = 1 (The difference of two numbers is 1)

2. xy = 6 (The product of the two numbers is 6)

We can solve this system of equations step by step:

Step 1: Solve the first equation for x: x = y + 1

Step 2: Substitute x in the second equation: (y + 1)y = 6, which simplifies to y^2 + y - 6 = 0

Step 3: Factor the quadratic equation: (y - 2)(y + 3) = 0

Step 4: Set each factor equal to zero and solve for y: y - 2 = 0 gives y = 2 and y + 3 = 0 gives y = -3

Step 5: Substitute y = 2 and y = -3 into the equation x = y + 1 to find the corresponding x values: x = 2 + 1 = 3 and x = -3 + 1 = -2

So, the two pairs of numbers that satisfy the conditions are (3, 2) and (-2, -3).