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本刊1988年第1期“埃丢斯——莫都(Erd(?)s——Mordell)不等式的加强”一文将埃丢斯——莫都不等式加强为: P为△ABC内部或边上一点,PD′、PE′、PF′分别为∠BPC、∠APC、∠BPA的平分线,则PA+PB+PC≥2(PD′+PE′+PF′)。本文给出它的指数形式的推广: 定理设P为△ABC内部(或边界)上一点,记∠BPC、∠APC、∠BPA的角平分线长依次为t_a、t_b、t_c,PA=x、PB=y、PC=z,则 x~2+y~2+z~2≥2(t_a~2+t_b~2+t_c~2)。其中s≥1。证如图,设∠APB=2α、∠BPC=2β、
In the first issue of 1988, “Erds (-) s--Mordell’s intensification of inequality,” the paper adds the edes-mauer equation to: P is △ABC inside or on the edge One point, PD′, PE′, and PF′ are the bisectors of ∠BPC, ∠APC, and ∠BPA, respectively, and then PA+PB+PC≥2 (PD′+PE′+PF′). In this paper, the generalization of its exponential form is given: Theorem Let P be a point on △ABC internal (or boundary), and note that the angle bisectors of BPC, ∠APC, and ∠BPA are t_a, t_b, t_c, PA=x, respectively. PB=y, PC=z, then x~2+y~2+z~2≥2(t_a~2+t_b~2+t_c~2). Where s≥1. As shown in the figure, let ∠APB=2α, ∠BPC=2β,