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25 September, 16:35

Find two consecutive positive even numbers the sum of whose squares is 340

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  1. 25 September, 17:24
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    Consecutive even means

    x and x+2 since they are 2 apart

    sum of squares is 340

    x^2 + (x+2) ^2=340

    expand and add

    x^2+x^2+4x+4=340

    2x^2+4x+4=340

    divide both sides by 2 to make it easier

    x^2+2x+2=170

    minus 170 bot sides

    x^2+2x-168=0

    facotr

    (x-12) (x+14) = 0

    set each to zero

    x-12=0

    add 12

    x=12

    x+14=0

    minus 14

    x=-14

    but they has to e positive to disregard

    x=12

    x+2=14

    numbers are 12 and 14
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