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16 July, 14:35

What multiplies to - 900 and adds to 5?

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  1. 16 July, 14:59
    0
    Xy = - 900

    x + y = 5

    x + y = 5

    x - x + y = - x + 5

    y = - x + 5

    xy = - 900

    x (-x + 5) = - 900

    x (-x) + x (5) = - 900

    -x² + 5x = - 900

    -x² + 5x + 900 = 0

    -1 (x²) - 1 (-5x) - 1 (-900) = 0

    -1 (x² - 5x - 900) = 0

    -1 - 1

    x² - 5x - 900 = 0

    x = - (-5) ± √ ((-5) ² - 4 (1) (-900))

    2 (1)

    x = 5 ± √ (25 + 3600)

    2

    x = 5 ± √ (3625)

    2

    x = 5 ± 5√ (145)

    2

    x = 2.5 ± 2.5√ (145)

    x + y = 5

    2.5 ± 2.5 √ (145) + y = 5

    - (2.5 ± 2.5√ (145) - (2.5 ± 2.5√ (145)

    y = 2.5 ± 2.5√ (145)

    (x, y) = (2.5 ± 2.5√ (145), 2.5 ± 2.5√ (145))

    The two numbers that add up to 5 and multiply to - 900 are 2.5 ± 2.5√ (145).
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