xyh 发表于 2009-9-21 04:33:23

无理数证明

<br /="/"/><p>证明 2<sup>0.5</sup>+3<sup>0.5</sup>+5<sup>0.5  </sup>为无理数<div></div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></p>

HF: 发表于 2009-9-21 17:26:21

回复：无理数证明

<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>suppose the sum a is a rational numer.</div><div>so (sqrt(2)+sqrt(3))^2 = (a-sqrt(5))^2, from which we get</div><div>sqrt(6) = b+c sqrt(5), where b,c are rational numbers.</div><div>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.</div><div> </div><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>

xyh 发表于 2009-9-22 07:40:12

证明正确

<br /="/"/>  证明正确<br /="/"/><br /="/"/><br /="/"/><br /="/"/><br /="/"/><div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div>
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