Question 1043306: (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
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! What happens if you try this:
And the equation becomes  while the question becomes, which of the following cannot be the value of X ?
I do not know for certain if this approach is good, since the original equation will have an xy term, which rotates your hyperbola.
Answer by ikleyn(52797)  (Show Source):
You can put this solution on YOUR website! .
(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
~~~~~~~~~~~~~~
 = after transformations = 4xy.
If = = 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).
Solved.
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