高二數(shù)學(xué)理第五節(jié)三個(gè)正數(shù)的算術(shù)幾何平均不等式課件

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.二元基本不等式Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.

探究1：已知a、b、c∈R+,那么

a3+b3+c3≥3abc,當(dāng)且僅當(dāng)a=b=c時(shí),等號

成立。

[參考公式:(a+b)3=a3+3a2b+3ab2+b3;

a3+b3=(a+b)(a2-ab+b2)]Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.

探究2：請證明：當(dāng)a,b,c∈R+,那

么,當(dāng)且僅當(dāng)a=b=c時(shí),

等號成立。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.均值不等式：

二元均值不等式：

若a,b>0,則，當(dāng)且僅當(dāng)a=b時(shí),

等號成立；Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.均值不等式：

二元均值不等式：

若a,b>0,則，當(dāng)且僅當(dāng)a=b時(shí),

等號成立；三元均值不等式：若a,b,c>0,則

，當(dāng)且僅當(dāng)a=b=c時(shí),等號成立;Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.均值不等式：

二元均值不等式：

若a,b>0,則，當(dāng)且僅當(dāng)a=b時(shí),

等號成立；三元均值不等式：若a,b,c>0,則

，當(dāng)且僅當(dāng)a=b=c時(shí),等號成立;時(shí),等號成立；n元均值不等式：若a1,a2,…an>0,則

，當(dāng)且僅當(dāng)a1=…=anEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.例1.已知x、y、z∈R+,求(x+y+z)3≥27xyz.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.例2.已知a、b、c∈R+,求證Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.如圖,把一塊邊長是a的正方形鐵片的各角切去大小相同的小正方形,再把它的邊沿著虛線折轉(zhuǎn)做成一個(gè)無

蓋方底的盒子,向切去的正

方形邊長是多少時(shí),才能使

盒子的容積最大？xyEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.教材P10T14Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.***作業(yè)布置***