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

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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



User Debiasej
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