用反证法证明,一个有理数与一个无理数之和是无理数
人气:181 ℃ 时间:2019-08-31 18:22:13
解答
设a=p/q(p,q是整数,且互质)是有理数,b是无理数.
假设c=a+b是有理数,可设c=r/s(r,s是整数,且互质)
于是b=c-a=r/s-p/q=(qr-ps)/(sq)是有理数.矛盾!
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