y=(x^2+1)^2/4x
=(x^2+2x+1)/(4x)
=(x/4)+(1/2)+(1/4x)≥2√(x/4)*(1/4x)+(1/2)=(1/2)+(1/2)=1
当x/4=1/4x时,x=1
取得最小值：ymin=1