Question 1158007
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            This problem is nice.  But it becomes nice only in hands of those who knows how to solve it and
            knows how to present the solution to others in a way they see its beaty.


            It is not the way @josgarithmetic tries to do it:  he simply does not know the right way.


            By following his way,  you will  NEVER  feel its beauty.



<pre>
Let "a" be the middle term of the progression, and let "d" be its common difference.

Then the first term of the AP is  {{{a[1]}}} = d-a, and its third term is  {{{a[3]}}} = d+a.


Since the sum ot the three terms is equal to 42, you have this equation

    (a-d) + a + (a+d) = 42,   

or   3a = 42,  which immediately implies a = 42/3 = 14.


Thus we just found the middle terms, very quickly, easy and practically MENTALLY.


Next, regarding the product of the terms, we have this equation 

    (a-d)*(a+d) = 52,
or
    a^2 - d^2 = 52.

Substitute here  a = 14, the value found couple of lines above, and you will get

    d^2 = a^2 - 52 = 14^2 - 52 = 144;

therefore

    d = +/- {{{sqrt(144)}}} = +/- 12.


At this stage, the problem is just solved.


<U>ANSWER</U>.  For the three terms, there are two possibilities.

                 1)  The progression is  14-12 =  2,  14  and  14+12 = 26  ( with d = 12 ),  or

                 2)  The progression is  14+12 = 26,  14  and  14-12 = 2   ( with d = -12 ).

                 So, the second progression is simply the reversed first progression.
</pre>

Solved.


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It is how this problem is designed, is intended and is expected to be solved.