Question

证明无论m n为任何实数 m^4+6m^2+2n^2-4n+18的值恒大于0

Answer 1

m^4+6m^2+2n^2-4n+18

=（m^4+6m^2+9)+(2n^2-4n+9)

=(m^2+3)^2+2(n-1)^2+7

因为(m^2+3)^2+2(n-1)^2大于等于0

所以(m^2+3)^2+2(n-1)^2+7恒大于0