y=x√3-x^2
=-{x^2-x√3+[(√3)/2]^2-[(√3)/2]^2}
=-{x^2-x√3+[(√3)/2]^2}+[(√3)/2]^2
=-[x-(√3)/2]^2+3/4
-[x-(√3)/2]^2≤0
所以,当x=(√3)/2时,y有最大值3/4.