Re: [中學] 100中正高中教師甄選試題
※ 引述《RainIced (我好想念快速的宿網)》之銘言：
: 想問這四題怎麼寫，謝謝。
: 3. x^2 + (y-1)^2 = 1 ，求 (x+y+1)/(x-y+3) 之最小值？
x=cosθ=(1-t^2)/(1+t^2), y=1+sinθ=(1+t^2+2t)/(1+t^2)
(x+y+1)/(x-y+3)=u
(1-t^2+1+2t+t^2+1+t^2)=u(1-t^2-1-t^2-2t+3+3t^2)
(3+2t+t^2)=u(3-2t+t^2)
(1-u)t^2+2(1+u)t+3(1-u)=0
Δ=[(1+u)^2-3(1-u)^2]/(1-u)≧0
(-2u^2+8u-2)/(1-u)≧0
(u^2-4u+1)(u-1)≧0
(u-2+√3)(u-1)(u-2-√3)≧0
min (u)=2-√3
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