Re: [中學] 100台南二中教甄一題
※ 引述《forbeat (殘酷的現實面！)》之銘言：
: x+y+z=(1/x)+(1/y)+(1/z)=1，試證x,y,z至少有一個是1
: ps.請問南二中會放全部題目跟答案嗎？
: 考爆了想再算一遍 82分離我真遙遠.....
由 (1/x) + (1/y) + (1/z) = 1, 知 x,y,z 都不是 0,
且 xy + yz + zx = xyz, 設此共同值為 k.
由根與係數關係，得 x,y,z 為三次方程式 t^3 - t^2 + k t - k = 0.
而此三次方程式容易看出有一根為 1, 故得證。
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