Question 1127469
.


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


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


<pre>
    If  {{{sqrt(x)}}} + {{{sqrt(y)}}} = {{{sqrt(45)}}}  and x and y are positive integers, then what is the value of {{{sqrt(x+y)}}} ?
</pre>


<U>Solution</U>


<pre>
{{{sqrt(x)}}} + {{{sqrt(y)}}} = {{{sqrt(45)}}}  ====>  


{{{sqrt(x)}}} = {{{sqrt(45)}}} - {{{sqrt(y)}}}  ====>  square both sides  ====>


x = {{{45}}} - {{{2*sqrt(45)*sqrt(y)}}} + {{{y}}}.   (*)


Since x and y  in this equation are <U>integers</U>,  {{{2*sqrt(45)*sqrt(y)}}} must be integer.


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


It implies that  y = 5.


Then from  (*)  x = {{{45 - 2*sqrt(45)*sqrt(5) + 5}}} = {{{45 - 2*15 + 5}}} = 20.


<U>Answer</U>.  If  {{{sqrt(x) + sqrt(y)}}} = {{{sqrt(45)}}}  and x and y are positive integers,  then  {{{sqrt(x+y)}}} = {{{sqrt(20+5)}}} = {{{sqrt(25)}}} = 5.
</pre>

Solved.



Nice solution to a nice problem.



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


<pre>
    We are given an info about the symmetric function  f(x,y) = {{{sqrt(x) + sqrt(y)}}}.


    Therefore, the question should be (and, actually, MUST BE) about a symmetric function, too;  in this case, about the function  {{{sqrt(x+y)}}}.
</pre>