SOLUTION: One pair of integers (x.y) solves {{{ sqrt( 4*sqrt( 7 )+11 )=y+sqrt( x ) }}}, find x*y.

square both sides:





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



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




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

We see if that checks in






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

Edwin