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21 December, 11:41

The product of two consecutive positive odd integers is 255. what are the integers?

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  1. 21 December, 12:37
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    Let the smaller odd positive integer be n.

    Then

    n (n+2) = 255

    solve by expanding to quadratic equation n^2+2n-255=0, reject negative root, or

    by trial and error: sqrt (255) = 15.97 = 16, so the odd integers should be 15, 17.

    Check: 15*17=255 ... correct!

    Alternatively, let the even number sandwiched between the odd integers be x.

    Then

    (x+1) (x-1) = 255

    x^2-1=255

    x^2=255+1=256

    x=sqrt (256) = 16

    so the required odd integers are 16-1=15, and 16+1=17.

    Your choice!
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