先化简,再求值:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737390d3e07422f989ccd1229c13ca6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
更新时间:2023-12-09 08:47:08
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解答题-计算题
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【推荐2】先阅读下面的解答过程,再解决问题
形如
的化简,只要我们找到两个数a、
,
使
,
,
这样
,
,
于是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a24dfecedc229dd7159f9921f3005f5.png)
举例:化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397297f49ce2094f88a97f0d8953a645.png)
解:这里
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d8ff50244476a0023d3bf3bdc0cf75.png)
∵
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e201392af4ae1577657b5f362c6d2c45.png)
即
,
,
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d0ba0c12b6c01ee36a8b96afb5c2d7.png)
用上述例题的方法化简:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce22e17fbe24452c625bdeba341fad4.png)
(2)
形如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22cd11ef0bb2ed7f227817f59739c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c12dcc8b621e55f451346e2aa428bb.png)
使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab04de6651256f6281e9f4c1dc3c7955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6028fc26ad632eb4273d22caec20cc0a.png)
这样
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9d8a43d49a3f2e4a3e58898160278e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b429877c4474c597eeda61965c849718.png)
于是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a24dfecedc229dd7159f9921f3005f5.png)
举例:化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397297f49ce2094f88a97f0d8953a645.png)
解:这里
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94174f37421d296a192b2df66c05f875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d8ff50244476a0023d3bf3bdc0cf75.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd165d2c1b724c242c17ee3a8a1d0e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e201392af4ae1577657b5f362c6d2c45.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c013a9642c9dc481f1f3f329c7e6dfe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b777fa51240fb986e9f1968eb728871.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d0ba0c12b6c01ee36a8b96afb5c2d7.png)
用上述例题的方法化简:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce22e17fbe24452c625bdeba341fad4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2fe68501b102a22f4b7bcef0019d24.png)
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