高二選修絕對(duì)值不等式講義

1、高二選修絕對(duì)值不等式講義.:原原點(diǎn)點(diǎn)的的距距離離到到的的點(diǎn)點(diǎn)數(shù)數(shù)軸軸上上坐坐標(biāo)標(biāo)為為的的幾幾何何意意義義的的絕絕對(duì)對(duì)值值實(shí)實(shí)數(shù)數(shù)AaaaOaxa.,:,的的長(zhǎng)長(zhǎng)度度即即線(xiàn)線(xiàn)段段兩兩點(diǎn)點(diǎn)之之間間的的距距離離數(shù)數(shù)軸軸上上的的幾幾何何意意義義則則為為在在數(shù)數(shù)軸軸上上的的對(duì)對(duì)應(yīng)應(yīng)點(diǎn)點(diǎn)分分別別任任意意兩兩個(gè)個(gè)實(shí)實(shí)數(shù)數(shù)ABBAbaBAba abxba AB.,等等之之間間的的關(guān)關(guān)系系可可以以考考察察對(duì)對(duì)于于實(shí)實(shí)數(shù)數(shù)babababa .,之間的關(guān)系之間的關(guān)系下面研究下面研究baba xOaba+bbabaab 有有當(dāng)當(dāng), 0)1(時(shí)時(shí)當(dāng)當(dāng)0)2( abbababai 有有時(shí)時(shí)當(dāng)當(dāng),0, 0)(xOaba+b

2、xOaba+bbababaii 有有時(shí)時(shí)當(dāng)當(dāng),0, 0)(xOaba+bbababaabiii 有有時(shí)時(shí)則則當(dāng)當(dāng),0, 0, 0)(.,0, 1等等號(hào)號(hào)成成立立時(shí)時(shí)當(dāng)當(dāng)且且僅僅當(dāng)當(dāng)則則是是實(shí)實(shí)數(shù)數(shù)如如果果定定理理 abbababaOxyabab+稱(chēng)為絕對(duì)值三稱(chēng)為絕對(duì)值三角不等式角不等式baba :用用代代數(shù)數(shù)方方法法證證明明ababab ,0:時(shí)時(shí)當(dāng)當(dāng)證證明明2)(baba 222baba 222bbaa baba 2)(ababab ,0時(shí)時(shí)當(dāng)當(dāng)2)(baba 222baba 222baba 222baba baba 2)(.,0,等號(hào)成立等號(hào)成立時(shí)時(shí)當(dāng)且僅當(dāng)當(dāng)且僅當(dāng) abbabababab

3、aba 那那么么是是實(shí)實(shí)數(shù)數(shù)如如果果,babababa 那那么么是是實(shí)實(shí)數(shù)數(shù)如如果果,., 0)(, 2等等號(hào)號(hào)成成立立當(dāng)當(dāng)且且僅僅當(dāng)當(dāng)那那么么是是實(shí)實(shí)數(shù)數(shù)如如果果定定理理 cbbacbbacacba定理定理2的幾何解釋的幾何解釋:cbbacaCABCBAcba ,之之間間時(shí)時(shí)在在點(diǎn)點(diǎn)當(dāng)當(dāng)點(diǎn)點(diǎn)所所對(duì)對(duì)應(yīng)應(yīng)的的點(diǎn)點(diǎn)分分別別為為在在數(shù)數(shù)軸軸上上cbbacaCAB ,之之間間時(shí)時(shí)不不在在點(diǎn)點(diǎn)當(dāng)當(dāng)點(diǎn)點(diǎn)abxABcCabxABcCabxABcC 53232,0 1 bayxbyax求求證證已已知知例例例例2 兩個(gè)施工隊(duì)分別被安排在公路沿線(xiàn)的兩個(gè)地兩個(gè)施工隊(duì)分別被安排在公路沿線(xiàn)的兩個(gè)地點(diǎn)施工點(diǎn)施工,這兩個(gè)地點(diǎn)分別位于公路路碑的第這兩個(gè)地點(diǎn)分別位于公路路碑的第10km和和第第20km處處.現(xiàn)要在公路沿線(xiàn)建兩個(gè)施工隊(duì)的共同臨現(xiàn)要在公路沿線(xiàn)建兩個(gè)施工隊(duì)的共同臨時(shí)生活區(qū)時(shí)生活區(qū),每個(gè)施工隊(duì)每天在生活區(qū)和施工地點(diǎn)之每個(gè)施工隊(duì)每天在生活區(qū)和施工地點(diǎn)之間往返一次間往返一次.要使