Question

求函数y=(x^4+3x^2+3)/(x^2+1)的最小值

Answer 1

y=[(x^4+x^2)+(2x^2+2)+1]/(x^2+1)

=x^2+2+1/(x^2+1)

=(x^2+1)+1/(x^2+1)+1

≥2根号[(x^2+1)/(x^2+1)+1

=3

所以,函数y=(x^4+3x^2+3)/(x^2+1)的最小值是3