x^2-y-2lnx^1/2=0
y=f(x)=x^2-2lnx^(1/2)
y'=2x-1/x=-1解得x=1/2
f(1/2)=1/4-ln(1/2)
P点的切线方程为y=-(x-1/2)+1/4-ln(1/2)即4x+4y-3+4ln(1/2)=0
P到直线 4x+4y+1=0的最小距离d=|-3+4ln(1/2)-1|/4√2=[1-ln(1/2)]/√2