√x-y-1+√x+y-5=√a+b-2009-√2009-a-b
要使得根号有意义,则√x-y-1,√x+y-5,√a+b-2009,√2009-a-b都必须≥0
∴x-y-1≥0
x+y-5≥0
a+b-2009≥0
2009-a-b≥0
a+b-2009=2009-a-b=0
a+b=2009
当a+b=2009时,√x-y-1+√x+y-5=0
∴x-y-1=0 x-y=1
x+y-5=0 x+y=5
x=3,y=2
a+b+x^y+y^x
=2009+3^2+2^3
=2026