新高考數(shù)學一輪復習百題刷過關專題08 基本不等式綜合必刷100題(原卷版)

專題08基本不等式綜合必刷100題任務一:善良模式(基礎)1-40題一、單選題1．已知SKIPIF1<0均為正實數(shù)，且滿足SKIPIF1<0，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知圓C1：x2＋y2＋4ax＋4a2－4＝0和圓C2：x2＋y2－2by＋b2－1＝0只有一條公切線，若a，b∈R且ab≠0，則SKIPIF1<0＋SKIPIF1<0的最小值為（）A．3 B．8 C．4 D．94．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．9 B．10 C．11 D．SKIPIF1<05．已知SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0處的切線與直線SKIPIF1<0平行，則SKIPIF1<0的最小值是（）A．2 B．3 C．4 D．56．已知直線SKIPIF1<0與圓SKIPIF1<0相切，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，則下列結論中正確的是（）A．SKIPIF1<0的最大值是SKIPIF1<0 B．SKIPIF1<0的最小值是SKIPIF1<0C．SKIPIF1<0的最小值是SKIPIF1<0 D．SKIPIF1<0的最小值是SKIPIF1<08．已知a，b為正實數(shù)，且滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．2 B．SKIPIF1<0 C．4 D．SKIPIF1<09．已知在SKIPIF1<0中，動點C滿足SKIPIF1<0，其中SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．若實數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知正數(shù)x，y滿足x2+2xy-3=0，則2x+y的最小值是（）A．1 B．3C．6 D．1212．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值是（）A．1 B．2 C．3 D．413．若SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．若正數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．SKIPIF1<0的內(nèi)角A，B，C的對邊分別為a，b，c，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0面積的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．216．設a，b為正數(shù)，若圓SKIPIF1<0關于直線SKIPIF1<0對稱，則SKIPIF1<0的最小值為（）A．9 B．8 C．6 D．1017．已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．已知SKIPIF1<0，則SKIPIF1<0的最小值是（）A．1 B．4 C．7 D．SKIPIF1<020．已知正數(shù)a，b滿足SKIPIF1<0，則SKIPIF1<0的最小值等于（）A．4 B．SKIPIF1<0 C．8 D．921．下列函數(shù)中最小值為4的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<022．若直線SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）被圓SKIPIF1<0截得弦長為SKIPIF1<0，則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．設SKIPIF1<0為正數(shù)，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．已知正實數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．在等比數(shù)列SKIPIF1<0中，SKIPIF1<0，則SKIPIF1<0的最大值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．已知實數(shù)a，b，c成等差數(shù)列，則點SKIPIF1<0到直線SKIPIF1<0的最大距離是（）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．227．實數(shù)a，b滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值是（）A．4 B．6 C．SKIPIF1<0 D．SKIPIF1<028．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<029．設SKIPIF1<0(其中0<x<y)，則M，N，P的大小順序是（）A．P<N<M B．N<P<MC．P<M<N D．M<N<P30．若函數(shù)SKIPIF1<0的圖象經(jīng)過點SKIPIF1<0，則SKIPIF1<0（）A．有最大值SKIPIF1<0 B．有最小值SKIPIF1<0 C．有最大值SKIPIF1<0 D．有最小值SKIPIF1<031．已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．4 B．6 C．9 D．1232．設SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值是（）A．1 B．2 C．3 D．433．設SKIPIF1<0均為正實數(shù)，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．8 B．16 C．9 D．634．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若不等式SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<035．已知實數(shù)SKIPIF1<0，則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<036．設SKIPIF1<0，則SKIPIF1<0的最小值是（）A．1 B．2 C．3 D．437．若x，y∈R＋，3x＋y—xy=0，則2x＋y的最小值為（）A．2SKIPIF1<0＋5 B．4SKIPIF1<0 C．12 D．638．若正數(shù)x，y滿足x2＋6xy－1＝0，則x＋2y的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<039．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為（）A．8 B．10 C．4 D．640．已知實數(shù)m，n滿足SKIPIF1<0，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0任務二:中立模式(中檔)1-40題1．已知SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關系是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知實數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．在SKIPIF1<0中，內(nèi)角SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的對邊分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0邊上的中線SKIPIF1<0長的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知實數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．如圖，在SKIPIF1<0中，C是SKIPIF1<0的中點，P在線段SKIPIF1<0上，且SKIPIF1<0.過點P的直線交線段SKIPIF1<0分別于點N，M，且SKIPIF1<0，其中SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<06．已知SKIPIF1<0，滿足SKIPIF1<0則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知實數(shù)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為（）A．1 B．27 C．8 D．98．若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．若SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．設SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．SKIPIF1<011．如圖，在平行四邊形SKIPIF1<0中，點SKIPIF1<0是SKIPIF1<0的中點，點SKIPIF1<0為線段SKIPIF1<0上的一動點，若SKIPIF1<0，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．212．若實數(shù)SKIPIF1<0，SKIPIF1<0，不等式SKIPIF1<0恒成立，則正實數(shù)SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．13 C．SKIPIF1<0 D．SKIPIF1<014．若a，b，c均為正實數(shù)，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．若正實數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．7 B．6 C．5 D．417．已知函數(shù)SKIPIF1<0沒有極值點，則SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．若SKIPIF1<0，SKIPIF1<0，平面內(nèi)一點SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最大值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．設正實數(shù)SKIPIF1<0滿足SKIPIF1<0，則當SKIPIF1<0取得最小值時，SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值是（）A．8 B．6 C．4 D．2第II卷（非選擇題）二、填空題21．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為______．22．若SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為________.23．已知正實數(shù)x，y，z滿足SKIPIF1<0，則SKIPIF1<0的最大值為________．24．已知正實數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為___________.25．已知對任意正實數(shù)SKIPIF1<0，SKIPIF1<0，恒有SKIPIF1<0，則實數(shù)SKIPIF1<0的最小值是___________.26．已知SKIPIF1<0，則SKIPIF1<0的最小值是__________．27．若實數(shù)x，y滿足SKIPIF1<0，則SKIPIF1<0的最小值為___.28．若不等式SKIPIF1<0對一切正實數(shù)SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的最小值為______．29．已知SKIPIF1<0，SKIPIF1<0且滿足SKIPIF1<0，則SKIPIF1<0的最小值為________．30．已知a，b為正實數(shù)，且SKIPIF1<0，則SKIPIF1<0的最小值為___________.31．已知實數(shù)x＞0，y＞0，且滿足x2y+xy2﹣11xy+8x+2y＝0，則x+y的取值范圍是________．32．已知SKIPIF1<0且滿足SKIPIF1<0，則SKIPIF1<0的最小值是___________.三、解答題33．已知a，b，SKIPIF1<0，求證：SKIPIF1<0．34．設aSKIPIF1<00，bSKIPIF1<00，a+b＝2．（1）證明：SKIPIF1<0≥4；（2）證明：a3+b3≥2．35．設函數(shù)SKIPIF1<0．（1）若SKIPIF1<0，求不等式SKIPIF1<0的解集；（2）若SKIPIF1<0（1）SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的最小值．36．已知a，SKIPIF1<0，且SKIPIF1<0，求證：SKIPIF1<0.37．設x、y為實數(shù)，若SKIPIF1<0，求SKIPIF1<0的最大值.38．設a>0，b>0，且SKIPIF1<0＋SKIPIF1<0＝1，求證：a＋2bSKIPIF1<0SKIPIF1<0＋SKIPIF1<0.39．已知函數(shù)SKIPIF1<0的最小值為SKIPIF1<0．(I)求SKIPIF1<0的值；(II)當SKIPIF1<0時，求證：SKIPIF1<0．40．已知SKIPIF1<0是正實數(shù).（1）證明：SKIPIF1<0；（2）若SKIPIF1<0，證明：SKIPIF1<0.任務三:邪惡模式(困難)1-20題1．已知三次函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，若SKIPIF1<0SKIPIF1<0，其中SKIPIF1<0，則SKIPIF1<0的最小值為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．設SKIPIF1<0，則SKIPIF1<0取得最小值時，SKIPIF1<0的值為（）A．SKIPIF1<0 B．2 C．4 D．SKIPIF1<04．已知SKIPIF1<0，則SKIPIF1<0的最大值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．SKIPIF1<05．若a，b均為正實數(shù)，則SKIPIF1<0的最大值為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．26．已知SKIPIF1<0的內(nèi)角SKIPIF1<0的對邊分別是SKIPIF1<0且SKIPIF1<0，若SKIPIF1<0為最大邊，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知正數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（改編）已知正數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<09．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．設SKIPIF1<0，SKIPIF1<0，若三個數(shù)SKIPIF1<0