美夢成真教甄討論區

不等式

x - y = x^3 + y^3 ＞ 0
(x^2 + λy^2) ≦ 1
(x - y)(x^2 + λy^2) ≦ x^3 + y^3
(x^2 + y^2) / (xy - y^2) ≧ λ

(x^2 + y^2) / (xy - y^2)
= [(x - y)^2 + 2xy] / [y(x - y)]
= [(x - y) / y] + [2x / (x - y)]
= [(x - y) / y] + [2y / (x - y)] + 2
≧ 2√2 + 2

λ 之最大值為 2√2 + 2