✔ 最佳答案
解數學題:αβγ=1/30,αβ+βγ+γα=1/3,α+β+γ=31/30,α<β<γ,α=? β=? γ=?
Sol
設α,β,γ為x^3+ax^2+bx+c=0之三根
α+β+γ=31/30
a=-31/30
αβ+βγ+γα=1/3
b=1/3
αβγ=1/30
c=-1/30
So
α,β,γ為 x^3-31x^2/30+x/3-1/30=0之三根
α,β,γ為 30x^3-31x^2+10x-1=0之三根
30x^3-31x^2+10x-1=0
(5x-1)(6x^2-5x+1)=0
(5x-1)((3x-1)(2x-1)=0
x=1/5 or x=1/3 or x=1/2
So
α=1/5,β=1/3,γ=1/2