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Find the two numbers.

Two numbers add to give 500 and multiply to give 47124. What is the difference between the two numbers?

Comments

  1. First, we can create two equations.

    x + 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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