Find the two numbers.
Two numbers add to give 500 and multiply to give 47124. What is the difference between the two numbers?
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First, we can create two equations.
ReplyDeletex + y = 500
xy = 47124
Now we can do this:
y = 47124/x
If we substitute this into the next equation, we get:
x + 47124/x = 500
47124/x = 500 - x
47124 = 500x - x²
- x² + 500x - 47124 = 0
x² - 500x + 47124 = 0
Now we can solve the quadratic using the quadratic formula.
x = (-b ± √(b² - 4ac)) / 2a
Now is we substitute in our values, we get:
x = (500 ± √(250000 - 188496)) / 2
x = (500 ± 248) / 2
x = 126, 374
Now we have our solutions:
126 and 374
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