∵sinx+√3 cosx=-a ∴ 2(sinx/2+√3 cosx/2)=-a
∴2(sinxcosπ/3+cosxsinπ/3)=-a ∴sin(x+π/3)=-a/2
∵x∈[0,π] ∴x+π/3∈[π/3,4π/3] ∴-√3/2＜-a/2＜1 ∴-2＜a＜√3