求解OMK问题

weisheng4321

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puangenlun

(sqrt5+7)^1/3 -(sqrt5-7)^1/3 is complex number

楼主是不是写错题目了？

weisheng4321

题目搞错了 @。@ 对不起

keeroro

let y=(sqrt(50)+7)^1/3- (sqrt(50)-7)^1/3

y^3+3y-14=0

therefore y=2

Allmaths

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weisheng4321 发表于 8-2-2012 04:27 PM

    Let a=((50)^(1/2)+7)^(1/3), b=((50)^(1/2)-7)^(1/3), then ab=1

(m/n)^3=(a-b)^3=14-3(a-b)=14-3(m/n)

Let x=m/n,

x^3+3x-14=0

therefore x=2