SOLUTION: If √x+√y=√45 and x and y are positive integers, then what is the value of √x+y?

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Question 1127469: If √x+√y=√45 and x and y are positive integers, then what is the value of √x+y?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

If and and are positive integers, then what is the value of ?
........solve for





then



Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

My reading of the problem is different from that of the tutor @MathLover1,

and my solution is different, too, as well as my answer.

    If   +  =   and x and y are positive integers, then what is the value of  ?


Solution

 +  =   ====>  


 =  -   ====>  square both sides  ====>


x =  -  + .   (*)


Since x and y  in this equation are integers,   must be integer.


Hence, the factor "y" must complement the number 45 to a perfect square.


It implies that  y = 5.


Then from  (*)  x =  =  = 20.


Answer.  If   =   and x and y are positive integers,  then   =  =  = 5.

Solved.


Nice solution to a nice problem.


---------------

Specially for the tutor @MathLover1,  I'd like to explain,  why I think that my reading of the problem is correct.

    We are given an info about the symmetric function  f(x,y) = .


    Therefore, the question should be (and, actually, MUST BE) about a symmetric function, too;  in this case, about the function  .



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