令y=x^(3/2)-3/2*x
∴y'=3/2*√x-3/2=3/2(√x-1),
∴当0≤x＜1,时y'＜0,为减函数
当x＞1时,y'＞0,为增函数,
x=1时,y=-1/2
∴函数y=x^(3/2)-3/2*x在[0,+∞)上,最小值为ymin=-1/2,
即X*√X-3/2X≥-1/2