Question 1043306
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(x+y)^2-(x-y)^2=72 
In the equation above, x and y are positive integers. Which of the following CANNOT be the value of x+y?
A) 9
B) 11
C) 19
D) 24
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<pre>
{{{(x+y)^2 - (x-y)^2}}} = after transformations = 4xy.


If  {{{(x+y)^2 - (x-y)^2}}} =  = 72,  then  4xy = 72,  then xy = 18,

and for integer positive  x  and  y  we have these and only these solutions:

(x,y) = (1,18), (2,9), (3,6), (6,3), (9,2) and (18,1).

Then  x+y has these and only these values: x+y = 19, 11, 9.

It can not be 24.

The answer is option D).
</pre>

Solved.