Question

如果实数M,N满足关系式m+n=4,求m^2+N^2的最小值

Answer 1

因为m+n=4,

所以m=4-n,

所以m^2+n^2

=(4-n)^2+n^2

=2n^2-8n+16

=2(n^2-4n+4-4)+16

=2(n-2)^2+8≥8,

所以m^2+n^2的最小值是8.