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精英家教網 > 初中數學 > 題目詳情
20、Assume that a,b,c,d are integers,and four equations (a-2b)x=1,(b-3c)y=1,(c-4d)z=1,w+100=d have always solutions x,y,z,w of positive numbers respectively,then the minimum of a is
2433

(英漢詞典:to assume假設;integer整數;equation方程;solutions (方程的)解;positive正的;respectively分別地;minimum最小值)!
分析:根據四個方程都有正的解可得a>2b,b>3c,c>4d,d>100,從而可得出d的最小值,進而可分別求得c、b、a的最小值.
解答:解:∵四個方程都有正的解,
∴a>2b,b>3c,c>4d,d>100,
∴可得dmin=101,
又∵c>4d=404,得出cmin=405,
b>3c=1215,得出bmin=1216,
a>2b=2432,得出amin=2433.
故答案為:2433.
點評:本題是結合英語考查的關于整數問題綜合運用的試題,比較新穎,解答本題的關鍵是理解題意,根據d>100得出d的最小值,進而依次求出c、b和a的最小值.
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