Question 1118777
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<pre>
It is a "joke" problem for advanced students.


It does not assume that you will restore the functions and solve equations.


But it assumes that you firmly know that 

    - the first function has a vertex at the point (a,b) with two branches going down perpendicularly and making angles 45 degrees with the axes;


    - the second function has a vertex at the point (c,d) with two branches going up perpendicularly and making angles 45 degrees with the axes.


Then you have a rectangle as the intersection of all the branches (I refer to the solution and the plot / (a sketch is just enough !) 
by @greenestamps), and the problem asks about  a+c.


Notice that  {{{(a+c)/2}}} is x-coordinate of the mid-point of one diagonal of the rectangle,  and it is the same  as x-coordinate 
of the mid-point of the other diagonal  {{{(2+8)/2}}} = 5.


Thus  {{{(a+c)/2}}} = 5  and,  hence,  a+c = 10.
</pre>

Solved.


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This solution is parallel to the final part of the @greenestamps solution,


but presented in other words/terms to provide better understanding for you.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>The major idea of the problem and the major idea of the solution is in that</U>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;it does not require any calculations (except the absolute minimum).