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
问题描述：
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
答
已知m²-2(√2)m+n²+2(√3)n+5=0，求(√5)m²+2n²的值
m²-2(√2)m+n²+2(√3)n+5=[m-(√2)]²+[n+(√3)]²=0
故m=√2，n=-√3；于是(√5)m²+2n²=2√5+6
答
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