SOLUTION: (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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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(39620)   (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(52800)   (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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