[代數][謝謝 thepiano 老師]

[LATEX]

代數求值得問題

[thepiano]

(α - 1)^3 + 2(α - 1) - 1 = 0
(β - 1)^3 + 2(β - 1) + 1 = 0
令 a = α - 1，b = β - 1
a^3 + 2a - 1 = 0
b^3 + 2b + 1 = 0
a^3 + b^3 + 2(a + b) = 0
(a + b)(a^2 - ab + b^2 + 2) = 0
a^2 - ab + b^2 + 2 ＞ 0
故 a + b = 0
α + β = 2

[LATEX]

a^2 - ab + b^2 + 2 =(a-b)^2+ab+2 為何必大於0?

[thepiano]

(a-b/2)^2+(3/4)b^2+2