Question 1107093
<pre>
{{{ sqrt( 4*sqrt( 7 )+11 )=y+sqrt( x ) }}}

square both sides:

{{{ 4*sqrt( 7 )+11 =(y+sqrt( x ))^2 }}}

{{{ 4*sqrt( 7 )+11 =y^2+2y*sqrt( x )+x }}}

Since x and y are integers we can set the integer terms
on the left equal to the integer terms on the right

{{{11 =y^2+x }}}

and we can set the irrational terms on the left equal to the
irrational terms n the right:


{{{ 4*sqrt( 7 ) =2y*sqrt( x ) }}}

It's quite obvious that to have integer solutions
x must be 7, and y must be 2.

We see if that checks in

{{{11 =y^2+x }}}
{{{11 =2^2+7 }}}
{{{11 =4+7 }}}
{{{11 =11 }}}

Yes it does, so x*y = 7*2 = 14

Edwin</pre>