f(x)=根号3（sin^2x-cos^2x）+2sinxcosx+a
=sin2x-根号3cos2x+a
=2(1/2sing2x-根号3/2cos2x)+a
=2sin(2x-π/6)+a
故a=3
最小值为-2+a=1
最小正周期为π