If the product of two consecutive odd integers is decreased by 3, the result is 12. How do you find the integers?

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Answer 1 · 2016-07-17T05:38:01

the integers are #3# and #5#
Also the integers are #-3# and #-5#

The solution

Let #2n+1# be the odd integer
Let #2n+3# be the next odd integer

#(2n+1)(2n+3)-3=12#

#4n^2+8n+3-3=12#

#4n^2+8n=12#

#n^2+2n=3#

#n^2+2n-3=0#

Solution by factoring

#(n-1)(n+3)=0#

#n-1=0#
#n=1#

Let #2n+1# be the odd integer which is equal #=3#
Let #2n+3# be the next odd integer which is equal #=5#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

At #n+3=0#

#n=-3#
Let #2n+1# be the odd integer which is equal #=-5#
Let #2n+3# be the next odd integer which is equal #=-3#

Checking: using odd numbers 3, and 5
#(2n+1)(2n+3)-3=12#
#(3)(5)-3=12#
#12=12" "#correct

Checking: using odd numbers -5, and -3
#(2n+1)(2n+3)-3=12#
#(-5)(-3)-3=12#
#12=12" "#correct

God bless....I hope the explanation is useful.