令∠ACD=θ
AE=Sin(θ+45°)*AC/sin(180°-∠A-θ-45°)=4(Sinθ+Cosθ)/Cosθ=4(tanθ+1)
tanθ=(x-4)/4
BD=4(tan(45°-θ)+1)=4((tanθ-1)/(1+tanθ)+1)=8tanθ/(1+tanθ)=8(x-4)/x
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=8(x-4)/x