(本題滿分16分,第(1)小題4分,第(2)小題6分,第(2)小題6分)
在平行四邊形
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中,已知過點
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的直線與線段
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分別相交于點
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。若

。
(1)求證:
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與
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的關(guān)系為
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;
(2)設(shè)
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,定義在
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上的偶函數(shù)
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,當(dāng)
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時
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,且函數(shù)
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圖象關(guān)于直線
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對稱,求證:
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,
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并求
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時的解析式;
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(3)在(2)的條件下,不等式
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在
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上恒成立,求實數(shù)

的取值范圍。
(1)

,…………………………………………2分

,從而

�!�4分
(2)當(dāng)

時,

。

圖像關(guān)于直線
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對稱,

,
…………………………………………………………5分

,又
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為偶函數(shù),

。
…………………………………………………………7分
設(shè)

,則
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,………………………………………8分
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,即
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。
…………………………………………………………10分
(3)不等式為

,…………………………………………12分

對
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恒成立,因此

。…………………………………………………………14分
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在
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上單調(diào)遞增,
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時其最大值為

,

,即


。……………………………………16分
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
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