2022高一·全国·专题练习
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1 . 阅读材料,解答问题:
我们可以利用解二元一次方程组的代入消元法解形如
的二元二次方程组,实质是将二元二次方程组转化为一元一次方程或一元二次方程来求解.其解法如下:
解:由②得:
③
将③代入①得:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1714027be9f26182ab66294263adf804.png)
整理得:
,解得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdfac2f5a0b9460d2d7624c0cad7a2c.png)
将
代入
得
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b5200bd6fb1226f25df9910d8a3cd2.png)
原方程组的解为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d50ffc2e556df09c64785f4a5e021f9.png)
(1)请你用代入消元法解二元二次方程组:
;
(2)若关于
的二元二次方程组
有两组不同的实数解,求实数
的取值范围.
我们可以利用解二元一次方程组的代入消元法解形如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e3b8d71418f5c403442e3622ff15f8.png)
解:由②得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daab03b1642f1ea187c94f62088ac0fd.png)
将③代入①得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1714027be9f26182ab66294263adf804.png)
整理得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b0b55c3297ce66c96d1559d76971f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdfac2f5a0b9460d2d7624c0cad7a2c.png)
将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdfac2f5a0b9460d2d7624c0cad7a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82e415812cca9545611c0faa0c01b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a61ce26a085d6795f14cc796261928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b5200bd6fb1226f25df9910d8a3cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d50ffc2e556df09c64785f4a5e021f9.png)
(1)请你用代入消元法解二元二次方程组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da525cadd9c7c74b9b8cd54e102358c.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d708cb763716467219215cdc0782c0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2a91645204925ba25b0992fedbdcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知抛物线
与双曲线
的交点A的横坐标是1,则关于x的不等式
的解是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bce5d244c8c4e504d66b27ce047a49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/10/005a7ba9-231c-4b35-8c3b-0ca01debbcaa.png?resizew=154)
A.![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
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解题方法
3 . 甲、乙同学分别解“已知
,若
,求
的最小值”的过程如下:
甲:由基本不等式得
,因为
,故有
,即有
,又
,故
;
乙:因为
,有
,
.
同学们,请通过思考用合适的方法求解下题:
已知
,
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ccbe255a7d973e1041d1476152b4dc.png)
求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c7501096f4be07c98e97e29db21a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407e4330cfdd5cd0bcfd4f3bd1a898e6.png)
甲:由基本不等式得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3d79e354cf1cf6c5bb0d043b68d07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c7501096f4be07c98e97e29db21a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca151609ac905d7afb1029e46871eb8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421b46658c918a524d2bac634a43439a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b90fe86747dc4b2db35a84a3fa1f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91aabebca1d156f88f56fd50f9fe5bbe.png)
乙:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c7501096f4be07c98e97e29db21a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08677c8308807e4dca6fd9410d301a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec42d8fad3691c5174f28306ddd63af.png)
同学们,请通过思考用合适的方法求解下题:
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ccbe255a7d973e1041d1476152b4dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43895441ab985675e2facdedf18575dc.png)
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