Question

证明；对于任意的实数m,n,都有m平方+4n平方-6m-4n+9的值不小于-1

Answer 1

因为

(m-3)^2+(2n-1)^2≥0

展开得

m^2-6m+9+4n^2-4n+1≥0

所以

m^2-6m+9+4n^2-4n≥-1