已知三个数成等差数列,首末项之积为中间项的5倍,后两项的和为第一项的8倍.求这三个数.【备注:上海教育出版社高二上数学练习册7.2A组第9题】谢谢\(^o^)/~
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![已知三个数成等差数列,首末项之积为中间项的5倍,后两项的和为第一项的8倍.求这三个数.【备注:上海教育出版社高二上数学练习册7.2A组第9题】谢谢\(^o^)/~](/uploads/image/z/3944228-68-8.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%89%E4%B8%AA%E6%95%B0%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E9%A6%96%E6%9C%AB%E9%A1%B9%E4%B9%8B%E7%A7%AF%E4%B8%BA%E4%B8%AD%E9%97%B4%E9%A1%B9%E7%9A%845%E5%80%8D%2C%E5%90%8E%E4%B8%A4%E9%A1%B9%E7%9A%84%E5%92%8C%E4%B8%BA%E7%AC%AC%E4%B8%80%E9%A1%B9%E7%9A%848%E5%80%8D.%E6%B1%82%E8%BF%99%E4%B8%89%E4%B8%AA%E6%95%B0.%E3%80%90%E5%A4%87%E6%B3%A8%EF%BC%9A%E4%B8%8A%E6%B5%B7%E6%95%99%E8%82%B2%E5%87%BA%E7%89%88%E7%A4%BE%E9%AB%98%E4%BA%8C%E4%B8%8A%E6%95%B0%E5%AD%A6%E7%BB%83%E4%B9%A0%E5%86%8C7.2A%E7%BB%84%E7%AC%AC9%E9%A2%98%E3%80%91%E8%B0%A2%E8%B0%A2%5C%28%5Eo%5E%29%2F%7E)
已知三个数成等差数列,首末项之积为中间项的5倍,后两项的和为第一项的8倍.求这三个数.【备注:上海教育出版社高二上数学练习册7.2A组第9题】谢谢\(^o^)/~
已知三个数成等差数列,首末项之积为中间项的5倍,后两项的和为第一项的8倍.求这三个数.
【备注:上海教育出版社高二上数学练习册7.2A组第9题】谢谢\(^o^)/~
已知三个数成等差数列,首末项之积为中间项的5倍,后两项的和为第一项的8倍.求这三个数.【备注:上海教育出版社高二上数学练习册7.2A组第9题】谢谢\(^o^)/~
a1×a3=5a2 → a1(a1+2d)=5(a1+d) ①
a2+a3=8a1 → a1+d+a1+2d=8a1 ②
得3d=6a1 d=2a1③
③代入① a1(a1+4a1)=5(a1+2a1)
5(a1)²-15a1=0 5a1(a1-3)=0
最终得
a1=0 a1=3
d=0 d=6
∴等差数列为0,0,0或3,9,15