求4m^2+9n^2+4m+6n+10的最小值

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求4m^2+9n^2+4m+6n+10的最小值求4m^2+9n^2+4m+6n+10的最小值求4m^2+9n^2+4m+6n+10的最小值4m^2+9n^2+4m+6n+10=4m²+4m+

求4m^2+9n^2+4m+6n+10的最小值
求4m^2+9n^2+4m+6n+10的最小值

求4m^2+9n^2+4m+6n+10的最小值
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

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