已知:A、B是两个整式,
,
,
猜测:嘉淇猜测“无论a为何值,
始终成立”.
验证:请证明嘉淇猜测的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dfd36409bb9bc8dd98ae386893c01ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65ea5aed45aebd7adbea41dd2398707.png)
猜测:嘉淇猜测“无论a为何值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca51be437b1a97ca92aa1159ab71102c.png)
验证:请证明嘉淇猜测的结论.
更新时间:2023-06-19 17:25:36
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解答题-问答题
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【推荐1】【教材呈现】下题是华师版七年级上册数学教材第117页的部分内容.
代数式
的值为9,则代数式
的值为_______.
【阅读理解】小明在做作业时采用的方法如下:
由题意得
,则有
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e109543e309a7ca51eb7b12a401006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f377d50cc6bb039d37b8a30da2e719a.png)
.
所以代数式
的值为9.
【方法运用】
(1)若代数式
的值为15,求代数式
的值.
(2)若
时,代数式
的值为11,当
时,求代数式
的值.
【拓展应用】若
,
,则代数式
的值为_______.
代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276f1476f05176c3af5d8a56b219b988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a692fad5c4321198606f50161d2a22b.png)
【阅读理解】小明在做作业时采用的方法如下:
由题意得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03dd79e4dd670be2e395c3f0996fc26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa136be151fb4c1df30616ab3f0b1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e109543e309a7ca51eb7b12a401006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f377d50cc6bb039d37b8a30da2e719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6cb46e10f1e2510d42180999254eef.png)
所以代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a692fad5c4321198606f50161d2a22b.png)
【方法运用】
(1)若代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b0c4e284c862e67d6f03489ccebaf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e3db568b90cd02722c87b6ce0f0697.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a9620be4e9083fabe5a03b828478f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e37f58805d211475bd707f8ce4f1c32.png)
【拓展应用】若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e314233d40405e33e7a815f8c28ab9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a270df23b0706987b9807ebdb490c9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea873dd83b01dcdd9071a19d8899fce5.png)
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