已知函数f(x)=a/2x^2-2x+(a-4)lnx,a＞0,若函数在（1,2）上有极值,求a的取值范围.

f'(x)=ax-2+(a-4)/x=[ax^2-2x+(a-4)]/x设g(x)=ax^2-2x+(a-4)函数f(x)在（1,2）上有极值即g(x)=ax^2-2x+(a-4)在（1,2）有零点设g(x)=ax^2-2x+(a-4)在（1,2）没有零点当Δ=4-4a(a-4)2+√5当Δ=4-4a(a-4)>=0时0=0∴a>=3或g(1)