The product of two consecutive odd integers is 29 less than 8 times their sum. Find the two integers. Answer in the form of paired points with the lowest of the two integers first?

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Answer 1 · 2018-05-11T06:24:38

# (13, 15) or (1, 3)#

Let #x# and #x+2# be the odd consecutive numbers, then

As per the question, we have

#(x)(x + 2) = 8(x + x + 2) - 29#

#:. x^2 + 2x = 8(2x + 2) - 29#

#:. x^2 + 2x = 16x + 16 - 29#

#:. x^2 + 2x - 16x - 16 + 29 = 0#

#:. x^2 - 14x + 13 = 0#

#:. x^2 -x - 13x + 13 = 0#

#:. x(x - 1) - 13(x - 1) = 0#

#:. (x - 13)(x - 1) = 0#

#:. x = 13 or 1#

Now,

CASE I : #x = 13#

#:. x + 2 = 13 + 2 = 15#

#:.# The numbers are (13, 15).

CASE II : #x = 1#

#:. x + 2 = 1+ 2 = 3#

#:.# The numbers are (1, 3).

Hence, as there are two cases being formed here; the pair of numbers can be both (13, 15) or (1, 3).