Question

已知m^2-2*根号2m+n^2+2根号3n+5=0,求根号5m^2+2n^2的值

Answer 1

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