阅读下面的材料,并解决问题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0b72bbb54d2e17f27c51ce96c33e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0cd29a728ce265de971772228bec47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b762d7db221e677adcea7451ae81a39.png)
(1)观察上式并填空:
= ;
(2)观察上述规律并猜想:当
是正整数时:
= (用含
的式子表示)
(3)请利用(2)的结论计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0b72bbb54d2e17f27c51ce96c33e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0cd29a728ce265de971772228bec47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b762d7db221e677adcea7451ae81a39.png)
(1)观察上式并填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc88b05855e92ae1cd35173db570555.png)
(2)观察上述规律并猜想:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bdaf3f00985ae0b9f48dfad8ff8358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)请利用(2)的结论计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940d17abdecb61cf278f7d3d852b012c.png)
更新时间:2022-05-25 20:03:16
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相似题推荐
解答题-计算题
|
较易
(0.85)
【推荐1】先阅读下面的材料,再解答下列问题.
∵
,
∴
.
特别地,
,
∴
.
当然,也可以利用
,得
,
∴
.
这种变形叫做将分母有理化.
(1)观察上面的解答过程,请直接写出:
________;
________;
探索其规律:
________;(
的整数)
(2)利用上述思路方法计算:
.
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7064d3df15271ff3d05dc47d0578de9.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6ae0bab6e703f42cb50d8005bcc8b0.png)
特别地,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e3cec1d4d97ef6f42e4808df989931.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d24a11d8f494819d418e7fbbe83fb1.png)
当然,也可以利用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b742b70c0718481a5f0637f57bf03d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afd1117af9f297e7398b96ffcdaf3f0.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0525be1c1d65c4154836c327e38b22.png)
这种变形叫做将分母有理化.
(1)观察上面的解答过程,请直接写出:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64094954b7b132587efe89aa7f6f873b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26095d273862b9ae3c9e0acb114e9263.png)
探索其规律:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42388221a8b19545db7aa38fdf50d129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
(2)利用上述思路方法计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4025080eadf115ea5afafb486905b0d4.png)
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