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23 April, 15:50

One number is 5 greater than another. The product of the numbers are 84. Find both the two positive and two negative sets of numbers.

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  1. 23 April, 15:56
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    Let x, y be the two numbers.

    Given that one number is 5 greater than another.

    Let x be the smaller number ans y be the greater number.

    That is y=x+5. Let this be the first equation.

    And also given that product of the two numbers is 84.

    That is x*y = 84, let us plugin y=x+5 here.

    x * (x+5) = 84

    x^2 + 5x - 84 = 0.

    x^2+12x-7x-84 = 0

    x (x+12) - 7 (x+12) = 0

    (x-7) (x+12) = 0

    That is x = 7 or - 12.

    If x=7, y = 7+5=12.

    If x=-12, y = - 12+5 = - 7.

    Hence two positive numbers corresponding to given conditions are 7,12.

    And two negative numbers corresponding to given conditions are - 12,-7.
  2. 23 April, 16:07
    0
    GIVEN

    one number is greater than the other by 5.

    the product of both are 84.

    find out the number.

    To proof =

    let assume that one number be x

    other number be x+5

    the equation becomes

    ⇒ x (x+8) = 84

    ⇒ x²+5x-84 = 0

    ⇒ x² + 12x-7x-84 = 0

    ⇒ (x-7) (x+12) = 0

    ⇒x=7, x=-12

    now the positive numbers are 7 and 12

    now the negative numbers are - 12 and - 7

    hence proved
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