See if you can solve this tough one! Show work.

OMMGG, My tummy hurts just lookin' at that!

Theoretically, it could be any positive number as X and Y are undefined and no negative can be under a square root.

BOOOOOOOOOOOM!!!!!

ALAHUAKBAAARRR ???

this one 1+x+1+1*3(1241:121343 = 92011224 find x!

Another way to write this is 

$x=(x^2-y)^{2016!}$

x and y must both be integers

If x=0 and y=0    then 0=0  that works

If   $x=1\;\;and\;\;x^2-y=\pm1$   

that would work to if they are both integers that is

1-y=1

y=0

so

if  x=1 and y=0  that works too

1-y=-1

2=y

so

if x=1 and y=2  that will work

and that is it     

so the 3 answers are   (0,0)   (1,0)  and  (1,2)         

So x+y  = 0 or 1 or 3

Maybe another mathematician can do it a different / better way  ??

Your seconds question makes no sense to me.       :(

Oops sorry Melody $x=9y$

Also can I have a proof?