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.