新高考数学一轮复习精讲精练2.2 基本不等式（基础版）（原卷版）

2.2基本不等式（精讲）（基础版）思维导图思维导图考点呈现考点呈现例题剖析例题剖析考点一直接型【例1-1】（2022·江西）当SKIPIF1<0时，SKIPIF1<0的最小值为（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022·北京·高三学业考试）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．1 B．2 C．3 D．4【例1-3】（2022·广东）已知正实数a，b，满足条件2a+b=1，则ab的最大值为（

）A．4 B．8 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南驻马店）已知a>0，则当SKIPIF1<0取得最小值时，a的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．32．（2021·江苏）若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值是（

）A．4 B．SKIPIF1<0 C．9 D．183．（2021·河南南阳）下列函数中，最小值为2的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考点二常数替代型【例2-1】（2022·甘肃武威·高二期末（理））已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·湖南·长沙一中高三阶段练习）已知p，q为正实数且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南郑州）已知实数a>0，b>0，SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·山西太原）已知SKIPIF1<0为正实数，SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．43．（2022·全国·高三专题练习）已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·重庆巴蜀中学高三阶段练习）已知正实数a，b满足SKIPIF1<0，则SKIPIF1<0的最小值是（）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．6考点三配凑型【例3-1】（2022·全国·高三专题练习）函数SKIPIF1<0SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例3-2】（2021·辽宁）已知正实数x，则SKIPIF1<0的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-3】（2021·河北邢台）若SKIPIF1<0，则SKIPIF1<0的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全国·高三专题练习（理））若SKIPIF1<0，则SKIPIF1<0有（

）A．最大值SKIPIF1<0 B．最小值SKIPIF1<0 C．最大值SKIPIF1<0 D．最小值SKIPIF1<02．（2022·山西·怀仁市第一中学校二模）函数SKIPIF1<0的最小值为（

）A．8 B．7 C．6 D．53．（2022·江苏徐州）设SKIPIF1<0，SKIPIF1<0为正数，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点四消元型【例4】（2022·重庆·西南大学附中）已知正实数SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最大值为______.【一隅三反】1．（2022·北京·人大附中高三阶段练习）已知正数SKIPIF1<0、SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最小值是___________.2．（2020·江苏·高考真题）已知SKIPIF1<0，则SKIPIF1<0的最小值是_______．3．（2021·安徽·泾县中学高一阶段练习）设正实数SKIPIF1<0、SKIPIF1<0、SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最大值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点五求参范围【例5】（2022·全国·高三专题练习）若对任意SKIPIF1<0恒成立，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全国·高三专题练习）当SKIPIF1<0时，不等式SKIPIF1<0恒成立，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全国·高三专题练习）若对任意SKIPIF1<0，SKIPIF1<0恒成立，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全国·高三专题练习）若SKIPIF1<0，且SKIPIF1<0恒成立，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02.2基本不等式（精练）（基础版）题组一题组一直接型1．（2022·全国·课时练习）设x，y满足SKIPIF1<0，且x，y都是正数，则SKIPIF1<0的最大值是()A．400

B．100

C．40

D．202．（2021·重庆）已知两个正数SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．3 B．6 C．SKIPIF1<0 D．SKIPIF1<03．（2021·云南·砚山县第三高级中学）已知正实数SKIPIF1<0、SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南濮阳）若a>0，b>0，a，b的等差中项是1，且SKIPIF1<0的最小值为（

）A．1 B．2 C．3 D．45．（2022·河南南阳）已知SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，则SKIPIF1<0的最大值为（

）A．2 B．5 C．SKIPIF1<0 D．SKIPIF1<06．（2022·河南）已知公差不为0的等差数列SKIPIF1<0中，SKIPIF1<0（m，SKIPIF1<0），则mn的最大值为（

）A．6 B．12C．36 D．487．（2022·广东茂名）若a，b都为正实数且SKIPIF1<0，则SKIPIF1<0的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·山西）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最大值为（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．19．（2022·广东·深圳市高级中学）设正实数SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最大值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·北京大兴）当SKIPIF1<0时，SKIPIF1<0的最大值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0题组二题组二常数替代型1．（2022·安徽·高三阶段练习）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值是（

）A．1 B．2 C．4 D．62．（2022·河南·许昌高中）已知a，b为正实数，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．1 B．6 C．7 D．SKIPIF1<03．（2022·辽宁·沈阳二中二模）已知a，b为正实数，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．1 B．2 C．4 D．64．（2022·福建·模拟预测）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．13 B．19 C．21 D．275．（2022·天津·高三专题练习）若正实数SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0的最小值是（

）A．4 B．SKIPIF1<0 C．5 D．96．（2022·全国·高三专题练习）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·全国·高三专题练习）实数SKIPIF1<0，SKIPIF1<0且满足SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全国·高三专题练习）若SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．1 C．2 D．49．（2022·全国·高三专题练习）已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·广东珠海·高三期末）非负实数x，y满足SKIPIF1<0，则SKIPIF1<0的最小值为______．11．（2022·重庆长寿·高三期末）已知SKIPIF1<0，则SKIPIF1<0的最小值为______．题组三题组三配凑型1．（2022·全国·高三专题练习）函数SKIPIF1<0的最大值为（

）A．3 B．2 C．1 D．-12．（2022·全国·高三专题练习）若函数SKIPIF1<0在SKIPIF1<0处取最小值，则SKIPIF1<0（

）A．SKIPIF1<0 B．2 C．4 D．63．（2022·全国·高三专题练习）若SKIPIF1<0，则SKIPIF1<0有（

）A．最大值SKIPIF1<0 B．最小值SKIPIF1<0 C．最大值2 D．最小值24．（2022·安徽省蚌埠第三中学）已知x>3，则对于SKIPIF1<0，下列说法正确的是（

）A．y有最大值7 B．y有最小值7 C．y有最小值4 D．y有最大值45．（2022·安徽省舒城中学）若SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．4 B．3 C．2 D．16．（2022·甘肃·兰州市第二中学）若SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·全国·高三专题练习）若SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·江西新余）已知正实数x，y满足4x+3y＝4，则SKIPIF1<0的最小值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2022·全国·高三专题练习）设SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．SKIPIF1<0题组四题组四消元型1．（2022·河南·郑州四中）已知a＞0，且a2－b＋4＝0，则SKIPIF1<0（

）A．有最大值SKIPIF1<0 B．有最大值SKIPIF1<0 C．有最小值SKIPIF1<0 D．有最小值SKIPIF1<02．（2022·辽宁丹东）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．33．（2022·山东临沂）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0有（

）A．最大值SKIPIF1<0 B．最小值SKIPIF1<0 C．最大值SKIPIF1<0 D．最小值SKIPIF1<04．（2022·全国·高三专题练习）设正实数SKIPIF1<0，SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，则当SKIPIF1<0取得最大值时，SKIPIF1<0的最大值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2021·江苏·常州市北郊高级中学）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0最大值为______．题组五题组五求参范围1．（2022·浙江·高