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1 March, 05:15

What two numbers multiply to - 96 and add to 7

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  1. 1 March, 05:27
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    The numbers are x and y.

    Therefore, we can suggest this system of equations:

    xy=-96

    x+y=7 ⇒x=7-y

    solve this systeme by substitution method.

    (7-y) y=-96

    7y-y²=-96

    y²-7y-96=0

    We solve this square ecuation:

    y=[7⁺₋√ (49-4 (1) (-96)) ] / 2 = (7⁺₋√433) / 2

    We have two solutions:

    y₁ = (7-√433) / 2 (y₁≈-6.904326 ...)

    x₁=7-y₁

    x₁=7 - (7-√433) / 2 = (7+√433) / 2 (x₁≈13.904326 ...)

    y₂ = (7+√433) / 2 (y₂≈13.904326 ...)

    x₂=7-y₂

    x₂=7 - (7+√433) / 2 = (7-√433) / 2 (x₂≈-6.904326 ...)

    Therefore:

    The numbers are (7-√433) / 2 and (7+√433) / 2.
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