我们可以从解方程的角度理解从有理数扩充到实数的必要性.若
不是某个有理数的平方,则方程
在有理数范围内无解;若
不是某个有理数的立方,则方程
在有理数范围无解.而在实数范围内以上方程均有解,这是扩充数的范围的一个好处.根据你对实数的理解,选出正确命题的序号__________ .
①
在实数范围内有解;②
在实数范围内的解不止一个;③
在实数范围内有解,解介于1和2之间;④对于任意的
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84844229661e4c8bcfcc845c73ae8bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478dceaa58f0cd0fea61f9130ecf0845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea727365a3f3f64a75a0dfb94bb5536c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb58a7295c7697e8874497241c79261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a0cbdb16c403765391cd2866456e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7899d3f88d931cf665475db58de94e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84844229661e4c8bcfcc845c73ae8bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c574fa6f472806527f6f7921bad9ef.png)
更新时间:2021-05-13 16:10:54
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