由題意可知：Δ=(-a)²-4(a²-a+1/4)=4a-1≥0
即得：a≥1/4
由韋達定理有：x1+x2=a,x1*x2=a²-a+ 1/4
那么：(x1x2)/(x1+x2)
=(a²-a+ 1/4)/a
=a - 1 + 1/(4a)
=a+ 1/(4a) -1
由均值定理得：a+ 1/(4a)≥2根號[a*1/(4a)]=1 （當(dāng)且僅當(dāng)a=1/(4a)即a=1/2時取等號）
所以當(dāng)a=1/2時,a+ 1/(4a)有最小值為1,此時對應(yīng)(x1x2)/(x1+x2)的最小值為0.