tanxα,tanβ是方程x^2+3根号3x+4=0两根,且α,β属于（-π/2,π/2),则α+β=?

tanxα,tanβ是方程x^2+3根号3x+4=0两根,且α,β属于（-π/2,π/2),则α+β=?
tanxα,tanβ是方程x^2+3根号3x+4=0两根,且α,β属于（-π/2,π/2),则α+β=?

tanxα,tanβ是方程x^2+3根号3x+4=0两根,且α,β属于（-π/2,π/2),则α+β=?
tanα*tanβ=4,
tanα+tanβ=-3√3.
所以tanα<0,tanβ<0,
α,β∈(-π/2,0)
α+β∈(-π,0)
tan(a+β)=(tanα+tanβ)(1-tanαtanβ)=-3√3/(1-4)=-√3
所以a+β=-π/3

tanα+tanβ =-3 √3
tanα.tanβ =4
tan(α+β) =(tanα+tanβ)/(1-tanα.tanβ)
= -3√3/(1-4)
α+β = π/3