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1 April, 13:02

What two number mutiply to - 240 but add up to 8

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  1. 1 April, 13:20
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    Let us assume the two unknown numbers to be "x" and "y".

    Then

    xy = - 240

    x = - (240/y)

    And

    x + y = 8

    Now let us put the value of x in the second equation. We get

    x + y = 8

    - (240/y) + y = 8

    y^2 - 240 = 8y

    y^2 - 8y - 240 = 0

    y^2 - 20y + 12y - 240 = 0

    y (y - 20) + 12 (y - 20) = 0

    (y - 20) (y + 12) = 0

    So we can see that the unknown number y can have two values and hence the unknown number will also have two values.

    When

    y - 20 = 0

    y = 20

    Then

    xy = - 240

    20x = - 240

    x = - 12

    So we can see that when y is equal to 20 then x is equal to - 12 and when y is equal to - 12 then x is equal to 20. So the two numbers are 20 and - 12.
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