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18 April, 11:24

What multiplies to - 1 and adds to 2

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  1. 18 April, 15:14
    0
    xy = - 1

    x + y = 2

    x + y = - 2

    - x - x

    y = - x - 2

    xy = - 1

    x (-x + 2) = - 1

    x (-x) + x (2) = - 1

    -x² + 2x = - 1

    + 1 + 1

    -x² + 2x + 1 = 0

    -1 (x²) - 1 (-2x) - 1 (-1) = 0

    -1 (x² - 2x - 1) = 0

    -1 - 1

    x² - 2x - 1 = 0

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

    2 (1)

    x = 2 ± √ (4 - 4 (-1))

    2

    x = 2 ± √ (4 + 4)

    2

    x = 2 ± √ (8)

    2

    x = 2 ± 2√ (2)

    2

    x = 1 ± √ (2)

    x + y = 2

    (1 ± √ (2)) + y = 2

    - (1 ± √ (2)) - (1 ± √ (2))

    y = 1 ± √ (2)

    (x, y) = (1 ± √ (2), 1 ± √ (2))

    The numbers that multiply to - 1 and add to 2 are 1 ± √ (2).
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