the product of two consecutive positive even intergers is 14 more than their sum. Find the integers.

Question

the product of two consecutive positive even intergers is 14 more than their sum. Find the integers.

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    2021-10-11T01:59:52+00:00

    Answer:4 and six

    Step-by-step explanation: n
    =  the first number  (
    n
    +
    2
    )
    =  the second number  


    Set up an equation using the information  n
    ×  (
    n
    +
    2
    )
    =
    n
    +
    (
    n
    +
    2
    )
    +
    14  doing the operations gives.  

    n
    2  +  2
    n
    =  2
    n  +  16  Subtract  2
    n  from both sides

    n
    2
    + 2
    n
    −  2
    n  =
    2
    n  −
    2
    n  +
    16

    This results in   n
    2
    =  16

    Take the square root of both sides.

     √
    n
    2  =  ±  √
    16

    This gives  n
    =
    4  or  n
    =  −
    4

    The negative answer is invalid  n  =  4  add 2 to find  n
    +
    2
    ,  the second number

    4
    +
    2
    =
    6


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