Final answer:
The two positive numbers whose difference is 20 and whose product is 189 are 27 and 7, found by setting up a system of equations and solving them step-by-step.
Step-by-step explanation:
To find two positive numbers whose difference is 20 and whose product is 189, we can set up a system of equations:
By solving these equations, we find the numbers to be x = 21 and y = 1.
Step 1: From the first equation, we express one variable in terms of the other, x = y + 20.
Step 2: Substitute x in the second equation, (y + 20)y = 189.
Step 3: Expand the equation and solve the quadratic, y2 + 20y - 189 = 0.
Step 4: Factor the equation, (y - 7)(y + 27) = 0.
Step 5: Two possible solutions for y are y = 7 or y = -27. Since we need positive numbers, we take y = 7.
Step 6: Substitute y back into x = y + 20 to find x, x = 7 + 20 = 27.
Therefore, the two positive numbers are 27 and 7.