Since 1+α+β+γ = 0,the four vectors 1,α,β and γ form a rhombus such that the opposite vectors are opposites.In general,assuming α = -β,then γ = -1.
(1+α)(1+β)(1+γ)
= 1+α+β+γ+αβ+αγ+βγ+αβγ
= αβ+αγ+βγ+αβγ
= αβ(1+γ) + γ(α+β)
= 0
美国高中数学物理教师
Since 1+α+β+γ = 0,the four vectors 1,α,β and γ form a rhombus such that the opposite vectors are opposites.In general,assuming α = -β,then γ = -1.
(1+α)(1+β)(1+γ)
= 1+α+β+γ+αβ+αγ+βγ+αβγ
= αβ+αγ+βγ+αβγ
= αβ(1+γ) + γ(α+β)
= 0
美国高中数学物理教师