不等式知识点总结

①（对称性）abbaa,bcac②（传递性）③（可加性）abacbc（同向可加性）abcdacbd（异向可减性）abcdacbd,abc,0abc,0⑤（同向正数可乘性）ab0,cd0acbd（异向正数可除性）abdabcdc0nn(,1)ababnN且nab0ab(nN,且n1)nn1111ab（倒数法则）ab0;ab0abab22ab2bRab"".①222ab，bRabab,22.abb2abaab2abcabcR（(、、)abc3abc当且仅当3时取到等号）.abcbcabbR④a⑤a222bcabc(a0,b0,c0)abc333ba若ab0,则2abba若ab0,则2ab⑥bbm⑦ana1(abmn11aambnb同加则变小.⑧xaxaax.22a时，xaxaxx;22babab.a2abab22，abRaba1b122b""（即调和平均几何平均算术平均当a(ab)2abab222;.aba2b22221a...a(aa...a).a212222nn12nxyxy(xx)(yy)(x,y,x,yR).212122222212121122(ab)(cd)(acbd)(a,b,c,dR).adbc22222(aaa)(bbb)(ababab).2222222123123112233(aa...a)(bb...b)(abab...).2abnn22222212n12n1122设,,kk.a...a,bb...bc,c,...,cb,b,...,b是设a12n12n12n12n则abab...abacac...acabab...ab.1n2n1n11122nn1122nna...abb...ba或12n12n(x)f有xxf(x)f(x)xxf(x)f(x)x,x(xxf()或f().2121212112122222131(a)(a);2224211,,k2k(k221212(),(kN,k112kkkkkk1kkk1k2k(k1)bxc0(或0)(a0,b4ac0)ax22规律：f(x)0f(x)g(x)0g(x)“或”（时f(x)g(x)0f(x)g(x)00g(x)f(x)0f(x)0a(a0)f(x)a(a0)⑴f(x)⑵a2f(x)a2f(x)f(x)0f(x)0f(x)0⑶⑸f(x)g(x)或⑷g(x)0f(x)g(x)g(x)00g(x)f(x)[g(x2f(x)[g(x2f(x)0f(x)g(x)g(x)0f(x)g(x)1aag(x)f(x)g(x)0a1af(x)aaf(x)g(x)f(x)g(x)f(x)0a10a1logf(x)logg(x)g(x)0aaf(x)g(x)(x)0flogf(x)logg(x)g(x)0.aaf(x)g(x)(a0).a、含绝对值不等式的解法：⑴定义法：a⑵平方法：a(a0)f(x)g(x)f(x)g(x22aaxa(a①x②x③faxxa(a(x)g(x)g(x)f(x)g(x)(g(x)④f(x)g(x)f(x)g(x)f(x)g(x)(g(x)c02与0与0ac020b0,c时a0时a0ac020b0,c0