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标题: 无理数证明 [打印本页]

作者: xyh 时间: 2009-9-21 04:33
标题: 无理数证明

证明 2^0.5+3^0.5+5^0.5为无理数

作者: HF: 时间: 2009-9-21 17:26
标题: 回复：无理数证明

suppose the sum a is a rational numer.

so (sqrt(2)+sqrt(3))^2 = (a-sqrt(5))^2, from which we get

sqrt(6) = b+c sqrt(5), where b,c are rational numbers.

so (sqrt(6)-c sqrt(5))^2 = b^2, and we get: sqrt(30) is a rational number, which can not be true by 'standard' proof using prime decomposition.

作者: xyh 时间: 2009-9-22 07:40
标题: 证明正确

证明正确

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