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31 October, 07:12

What numbers multiply to 6 and add up to 9

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Answers (1)
  1. 31 October, 08:34
    0
    Xy = 6

    x + y = 9

    x + y = 9

    x - x + y = - x + 9

    y = - x + 9

    xy = 6

    x (-x + 9) = 6

    x (-x) + x (9) = 6

    -x² + 9x = 6

    -x² + 9x - 6 = 0

    -1 (x²) - 1 (-9x) - 1 (6) = 0

    -1 (x² - 9x + 6) = 0

    -1 - 1

    x² - 9x + 6 = 0

    x = - (-9) ± √ ((-9) ² - 4 (1) (6))

    2 (1)

    x = 9 ± √ (81 - 24)

    2

    x = 9 ± √ (57)

    2

    x = 4.5 ± 0.5√ (57)

    x + y = 9

    4.5 ± 0.5√ (57) + y = 9

    - (4.5 ± 0.5√ (57)) - (4.5 ± 0.5√ (57))

    y = 4.5 ± 0.5√ (57)

    (x, y) = (4.5 ± 0.5√ (57), 4.5 ± 0.5√ (57))

    The two numbers that multiply to 6 and add up to 9 are 4.5 ± 0.5√ (57).
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