我们定义一种新运算:a△b=a﹣b+ab.
(1)求2△(﹣3)的值;
(2)求(﹣5)△[1△(﹣2)]的值.
(1)求2△(﹣3)的值;
(2)求(﹣5)△[1△(﹣2)]的值.
更新时间:2017-10-13 08:59:16
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【知识点】 新定义下的实数运算
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解答题-计算题
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适中
(0.65)
【推荐1】【概念学习】
规定:求若干个相同的有理数(均不等于0)的除法运算叫做除方,如
,
等.类比有理数的乘方,我们把
记作
, 读作“2 的圈3次方”,
记作
,读作“-3的圈4次方”,一般地,把
记作
©,读作“
的圈c次方”.
(1)【初步探究】
直接写出计算结果:
________,
________,
(2)关于除方,下列说法错误的是 .
A. 任何非零数的圈2次方都等于1;
B. 对于任何正整数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/2018/12/26/2105179454029824/2105284085547008/STEM/7e209a560d8745a4a4e89991d0f29fc1.png?resizew=11)
;
C.
;
D. 负数的圈奇数次方结果是负数,负数的圈偶数次方结果是正数.
(3)【深入思考】 我们知道,有理数的减法运算可以转化为加法运算,除法运算可以转化为乘法运算,有 理数的除方运算如何转化为乘方运算呢?
![](https://img.xkw.com/dksih/QBM/2018/12/26/2105179454029824/null/STEM/37e42ff873e84b47a8df8d9606efac6a.png?resizew=277)
Ⅰ.试一试:仿照上面的算式,将下列运算结果直接写成幂的形式.
________;
________;
________.
Ⅱ.想一想:将一个非零有理数
的圈
次方写成幂的形式等于________;
Ⅲ.算一算:
________
规定:求若干个相同的有理数(均不等于0)的除法运算叫做除方,如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbfa18465de74e7a3a414704f38ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbada1b68a9ef62fa4375799eb9bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbfa18465de74e7a3a414704f38ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62ba56692ea408c868037cb082c5d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbada1b68a9ef62fa4375799eb9bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df1191c76b35c12934a6ba5bf43575c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb0eb6c7179e719476ac686b69b8a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)【初步探究】
直接写出计算结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cd02022523ccf7d70ad186993a102b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3967edd4be0613948c61d8a3d7dc4abe.png)
(2)关于除方,下列说法错误的是 .
A. 任何非零数的圈2次方都等于1;
B. 对于任何正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/2018/12/26/2105179454029824/2105284085547008/STEM/7e209a560d8745a4a4e89991d0f29fc1.png?resizew=11)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
C.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a052c2ae5f34e5b112e3068d2b08dd.png)
D. 负数的圈奇数次方结果是负数,负数的圈偶数次方结果是正数.
(3)【深入思考】 我们知道,有理数的减法运算可以转化为加法运算,除法运算可以转化为乘法运算,有 理数的除方运算如何转化为乘方运算呢?
![](https://img.xkw.com/dksih/QBM/2018/12/26/2105179454029824/null/STEM/37e42ff873e84b47a8df8d9606efac6a.png?resizew=277)
Ⅰ.试一试:仿照上面的算式,将下列运算结果直接写成幂的形式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f11c21c8f5868c175a7717fc44b2694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604184cd73c154614454529b2465fd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbc822bb9adc75e803d754255a54b1a.png)
Ⅱ.想一想:将一个非零有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
Ⅲ.算一算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b66c35c086660bec317c611a7f355d.png)
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解答题-问答题
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【推荐2】我们知道,任意一个有理数与无理数的和为无理数,任意一个不为零的有理数与一个无理数的积为无理数,而零与无理数的积为零.由此可得:如果
,其中
、
为有理数,
为无理数,那么
且
.
(1)如果
,其中
、
为有理数,那么
,
;
(2)如果
,其中
、
为有理数,求
的平方根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c5262da479816fd7f246d3637856b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34a27a3b570db87e8c880021ccf5441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55f025ed76fabbfd3d60ca69ff3f0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ec08be6e5edde3502faba89bb505e0.png)
您最近一年使用:0次