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