求4m^2+9n^2+4m+6n+10的最小值
问题描述：
求4m^2+9n^2+4m+6n+10的最小值
答
4m^2+9n^2+4m+6n+10=(2m+1)(2m+1)+(3n+1)(3n+1)+8
(2m+1)(2m+1)+(3n+1)(3n+1)=0
最小值为8
答
4m^2+9n^2+4m+6n+10
=4m²+4m+1+9n²+6n+1+8
=(2m+1)²+(3n+1)²+8
∴4m^2+9n^2+4m+6n+10的最小值是8