simple algebra

by observation one solution is {4,9}

i know the answer ......plz post the solution

let\, \, \sqrt{x}= t

let\, \, \sqrt{y}= u

solvin simultaneously we have

t + u^2 = 11
u + t^2 =7

we have
u^3 + ut =11 u ---1
u^3 + u^2t^2 = 7 u^2----2

1- 2
ut - u^2t^2 = 11u - 7u^2

t - ut^2 = 11 - 7u

solvin for u we have

u =\frac{t-11}{t^2-7}

substitutin for u we have
t^4 -14^2+t+38=0

we have t= 2 as a real root and three complex roots

for \,\, \, t= 2 \rightarrow x = 4

for \, t= 2 \rightarrow y = 11-t =11-2 = 9

complex roots u may see wolfram

btw hats off qwerty[123] !!!!!!!!!!!

http://www.goiit.com/posts/list/algebra-open-challenge-to-all-community-members-and-experts-73653.htm

sir complex solutons do exist na??

you are right, they will. But the problem as I see it appear time and again usually asks for real soutions only.