Question 1026395
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The product of two consecutive odd integers is 6 more than 5 times the smaller number, find both numbers
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        The "solution" in the post by @mananth is INCORRECT,

        since he incorrectly solved the quadratic equation.


        See my reasoning below.



<pre>
Let 'n' be the smaller of the two odd consecutive integers.
Then the greater add consecutive integer is (n+2).


Our equation is

    n*(n+2) = 5n + 6,

    n^2 + 2n = 5n + 6,

    n^2 - 3n - 6 = 0.


The discriminant is  d =  b^2 - 4ac = (-3)^2 - 4*1*(-6) = 9 + 24 = 33.


{{{sqrt(d)}}} = {{{sqrt(33)}}}  is not an integer or a rational number, 
so integer 'n' as described in the problem, does not exist.


<U>ANSWER</U>.  As posed/printed/presented in the post, the problem HAS NO solution.
</pre>

Solved correctly.