文档介绍：高中数学选修4-5知识点
高中数学 选修4--5知识点
1、不等式的基本性质
abba,,,?(对称性)
?(传递性) abbcac,,,,,
abacbc,,，,，?(可加性)
(同向可加性) a,b,c,d,a，c,b，d(异向可减性) a,b,c,d,a,c,b,d?(可积性) a,b,c,0,ac,bc
a,b,c,0,ac,bc
?(同向正数可乘性) abcdacbd,,,,,,0,0
ab(异向正数可除性) abcd,,,,,,0,0cd
nn?(平方法则) ababnNn,,,,,,0(,1)且
nn?(开方法则) ababnNn,,,,,,0(,1)且
1111a,b,0,,;a,b,0,,?(倒数法则) abab2、几个重要不等式
22ab，22ab,?"",abababR，,,2，,(当且仅当时取号). 变形公式:ab,. ，，2
ab，，ab,,ab(基本不等式) ,(当且仅当时取到等号). ?abR，,，，2
2ab，,,abab，,2变形公式: ab,.,,2,,
用基本不等式求最值时(积定和最小，和定积最大)，要注意满足三个条件“一正、二定、三相等”.
abc，，，3abc,,,abc?(三个正数的算术—几何平均不等式)(当且仅当时取到等号). ()abcR、、,3
222abcabbccaabR，，,，，,，? ，，
abc,,(当且仅当时取到等号).
333? abcabcabc，，,,,,3(0,0,0)
abc,,(当且仅当时取到等号).
ba若则ab,，,0,2?(当仅当a=b时取等号) ab
ba若则ab,，,,0,2(当仅当a=b时取等号) ab
bb，ma，na,,1,,?，(其中abmn,,,,000)，， aa，mb，nb
规律:小于1同加则变大，大于1同加则变小.
22? 当时，或axaxaxaxa,,,,,,,,0;
environment. In chicken diets composed of grain feed class and its by-products account for a considerable proportion. Such high total phosphorus content in feed, but most of its (65%~80%) combination of phosphorus and phytic acid (phytate), poultry low phytic acid phosphorus utilization capacity. According to reports, young birds of phytate phosphorus utilization is about 30%, adult birds is about 50%. Thus, phosphorus in plant feedstuffs alone cannot meet the needs of poultry would have to add inorganic phosphorus sources (mainly calcium hydrogen phosphate, bone meal, fishmeal, meat and bone meal also fall into this category), and total phosphorus in the diet increased. Today's lack of inorganic phosphorus sources throughout the world, has become the third more expensive feed ingredients in feed costs, 1 gram of inorganic phosphorus prices far beyond the price of 1 g of high quality protein. Increased feed costs on the one hand, and discharge large amounts of phosphorus from the waste, causing serious environmental pollution. When used in poultry feeding when high level of Cu and Zn, significantly increasing the fecal excretion of copper and zin