m^2-2√2m+n^2+2√3n+5=0
(m^2-2√2m+2)+(n^2+2√3n+3)=0
(m-√2)^2 (n-√3)^2 =0
m=√2,n=√3
所以,√5m^2 +2n^2=2√5+6