Re: [中學] <<< --- 大陸高中數學競賽 --- >>>
※ 引述《Sfly (topos)》之銘言：
: ※ 引述《diow1 (小玉)》之銘言：
: : 2 3
: : ω ω ω
: : ω是 1 的 7次方根 , 求 _______ + ________ + __________ = ???
: : 2 4 6
: : 1+ ω 1+ ω 1+ ω
: = 1/(w+1/w)+1/(w^2+1/w^2) + 1/(w^3+1/w^3)
: w satisfies 1+z+..+z^6=0,
: or z^3+1/z^3 + z^2+1/z^2 + z+1/z + 1 =0 .
: Let t = z+ 1/z, then
: t^3 - 3t + t^2 - 2 + t + 1 = 0
: t^3 + t^2 - 2t - 1 =0.
-->??????????????????????????
: thus, 1/(w+1/w)+1/(w^2+1/w^2) + 1/(w^3+1/w^3) = -2/1 = -2.
想問一下最後這一步驟
是怎麼推的呢?
有點看不太懂
謝謝^^
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