If the sum two numbers is 31 and their product is 240, then find the absolute difference between the numbers.

Sure, let's solve this step by step.

Step 1: Let's denote the two numbers as x and y. According to the problem, we have two equations:

x + y = 31 (equation 1) x * y = 240 (equation 2)

Step 2: We can express y from equation 1:

y = 31 - x

Step 3: Substitute y in equation 2:

x * (31 - x) = 240 31x - x^2 = 240 x^2 - 31x + 240 = 0

Step 4: Now we have a quadratic equation. We can solve it using the quadratic formula:

x = [31 ± sqrt((31)^2 - 41240)] / (2*1) x = [31 ± sqrt(961 - 960)] / 2 x = [31 ± sqrt(1)] / 2 x = [31 ± 1] / 2

So the solutions are x = 16 and x = 15.

Step 5: The absolute difference between the numbers is |x - y| = |16 - 15| = 1.