Question 33038
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Can you please solve this for me? I have to solve this using factoring:
The sum of the squares of two consecutive negative even integers is 340. Find the integers.
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        I will solve it in as simple way as I can.



<pre>
We are looking for two consecutive even integer numbers n and (n+2).


I will start from the central integer number 'm' between n and (n+2), so that

    n = m-1,  n+2 = m+1.


Then my equation is

    (m-1)^2 + (m+1)^2 = 340,

    (m^2 - 2m + 1) + (m^2 + 2m + 1) = 340,

     2m^2 + 2 = 340,

     2m^2 = 340 - 2 = 338,

      m^2 = 338/2 = 169,

      m = +/- {{{sqrt(169)}}} = +/- 13.


We are looking for two consecutive negative numbers, so these numbers are -14 and - 12.    <U>ANSWER</U>


<U>CHECK</U>.  (-14)^2 + (-12)^2 = 196 + 144 = 340.    ! Precisely correct !
</pre>

Notice that the other tutor reduced the problem to solution of a quadratic equation, but left the solution to you.


I solved the problem completely in a simplest way, practically mentally 
to the end, without solving a quadratic equation.