find two consecutive odd integers such that their product is 23 more than 5 times their sum.

Question

find two consecutive odd integers such that their product is 23 more than 5 times their sum.

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    2021-09-09T18:45:34+00:00

    If x is the smaller one, and is odd, the next consecutive odd integer is x+2.

    x(x+2) = 23 + 5(x+ (x+2))

    x^2 + 2x = 23 +5(2x+2)

    x^2 + 2x = 23 + 10x + 10

    x^2 -8x - 33 = 0

    (x-11)(x+3) = 0

    x = 11\textrm{ or }x=-3

    Check:

    11(13) = 143

    23 + 5(11 + 13) = 23 + 120 = 143, check

    -3(-1) = 3

    23 + 5(-3 + -1) = 3, check

    Answer: 11,13 or -3,-1

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