定义一种新的运算,观察下列各式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a750f78503f65d131a5f64f3c63de2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a94d11679913de1cf1a53425ece2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0422141c94634568f4775dfa234a9e.png)
;
(1)请你用代数式表示
的结果;
(2)小丁说:“
与
互为相反数”.小丁的说法正确吗?如果正确,请说明理由;如果不正确,请举例说明;
(3)若
,请计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a750f78503f65d131a5f64f3c63de2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a94d11679913de1cf1a53425ece2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0422141c94634568f4775dfa234a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95f9c973271f7448efd285785afa4dc.png)
(1)请你用代数式表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53e3bdb56a17481056d792c491cecd3.png)
(2)小丁说:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f247b8942bb6e86326bd83a3243ddd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84af31f064b2d0f453d7c597bbe522ab.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f286c3ac3326f90125eed2b1d53ea12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3151cda8b9fa7841b89b899811396773.png)
更新时间:2023-03-08 15:20:17
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解答题-问答题
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适中
(0.65)
名校
【推荐1】定义新运算:对于任意实数
,
,都有
,等式右边是通常的加法、减法及乘法运算.
(1)当
,且
时,求
与
的值;
(2)若
的值小于
,求
的取值范围,并在图中所示的数轴上表示出来.
![](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/88f8ccb6a5edecdac732888af7a4ae56.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/19/84f72373-6907-4ee8-b477-15d8abbf3ec9.png?resizew=300)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd9c827ec62d09c6c9b84d5571b25b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8aa4b942926be8ccad913c0cfd61bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4c05e18bac975a4c237a5426944f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】一般情况下
不成立,但有些数可以使得它成立,例如
.我们称使得
成立的一对数m,n为“相伴数对”,记为(m,n).
(1)试说明(1,-4)是相伴数对;
(2)若(x,4)是相伴数对,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf71b6fd41acc2bbbb9394a7b5e12242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c43f86ecb6bb6dfb3331b26d957d59d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf71b6fd41acc2bbbb9394a7b5e12242.png)
(1)试说明(1,-4)是相伴数对;
(2)若(x,4)是相伴数对,求x的值.
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【推荐2】已知有理数a、b、c在数轴上的位置如图所示,且
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/e33d6242-1305-435c-8eb6-944721f9aa02.png?resizew=162)
(1)根据数轴判断a、b、c、0的大小,并用“<”连接;
(2)由题意可知
_____;
(3)化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2fb9d9088cde5e02fc6f478c007ec5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/e33d6242-1305-435c-8eb6-944721f9aa02.png?resizew=162)
(1)根据数轴判断a、b、c、0的大小,并用“<”连接;
(2)由题意可知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892560dcff6af9f66a3f735652f69dd7.png)
(3)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d28c793382534c8a614076ddc9770bf.png)
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