The two positive numbers whose difference is 21 and whose product is 1080 are 54 and 33. We found these numbers by setting up a system of equations and factoring a quadratic equation.
Step-by-step explanation:
The student is asking for two positive numbers whose difference is 21 and whose product is 1080. We need to set up a system of equations to find these two numbers. Let's call the numbers x and y, with x being the larger number, then we can express the situation:
x - y = 21 (The difference between the numbers is 21)
x * y = 1080 (The product of the numbers is 1080)
We can solve these equations step by step:
From the first equation, we express y in terms of x: y = x - 21.
Substitute y in the second equation: x * (x - 21) = 1080.
Solve for x: x2 - 21x - 1080 = 0.
This can be factored into (x - 54)(x + 20) = 0, giving x = 54 or x = -20.
Since we are looking for positive numbers, we discard x = -20 and take x = 54.
Substitute x back into the first equation to find y: y = 54 - 21 = 33.
Therefore, the two positive numbers are 54 and 33.
The probable question can be: What are two positive numbers whose difference is 21, and the product of these numbers is 1080?