x>0时,
x+(1-x^2)/(3x)
=x+1/(3x)-(x/3)
=(2x/3)+1/(3x)
≥2√[(2x/3)·1/(3x)]
=(2√2)/3.
∴2x/3=1/(3x)→x=√2/2时,
所求最小值为:(2√2)/3.