Question 1139332
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<pre>
The idea is to express  (x+y)^2  via given data, and then take square root of this expression (of this number).

It will be exactly (x+y).


So,


{{{(x + y)^2}}} = {{{(x-y)^2}}} + 4xy = {{{(8*sqrt(2))^2}}} + 4*137 = 64*2 + 4*137 = 676.


Therefore, (x+y) = {{{sqrt(676)}}} = 26.


<U>ANSWER</U>.  x + y = 26.
</pre>

Answered and solved.