已知α，β∈(0，π)，且tanα,tanβ是方程x²-5x+6=0的两根.求:(1)α+β的值；(2)cos

(1)
tanα+tanβ=5
tanα.tanβ=6
tan(α+β) =(tanα+tanβ)/(1-tanα.tanβ)
= 5/(1-6)
=-1
α+β= 3π/4
(2)
tanα+tanβ=5
(sinαcosβ + cosαsinβ)/(cosα.cosβ) =5
sin(α+β)/(cosα.cosβ) =5
sin(3π/4)/(cosα.cosβ) =5
cosα.cosβ =√2/10
tanα.tanβ=6
sinα.sinβ = 6cosα.cosβ
=6√2/10
cos(α-β)
=cosα.cosβ + sinα.sinβ
=7√2/10