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?

Question

2391 views around the world

You can reuse this answer
Creative Commons License

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).