㏒1/2|x|< ㏒1/4|x+1|(解不等式)

熱心網(wǎng)友

首先化簡(jiǎn)右邊：㏒1/4|x+1|=㏒1/2|x+1|/㏒1/2(1/4)=0.5㏒1/2|x+1|原式相當(dāng)于：㏒1/2|x||x+1|討論:1、x+1≥0時(shí),相當(dāng)于:x^2＞x+1,x^2-x-1＞0,x＞(1+√5)/2,或-1≤x＜(1-√5)/22、x+1≤0時(shí)相當(dāng)于x^2＞-(x+1),因?yàn)閤^2+x+1＞0,△=-3＜0,所以x≤-1綜合上面得到：所以不等式的解是x＞(1+√5)/2∪x＜(1-√5)/2

熱心網(wǎng)友

1.化簡(jiǎn)原不等式得到：x^2|x+1|(且x不為0、x不為-1);2.利用數(shù)形結(jié)合，從函數(shù)：y=x^2　及函數(shù)：y=|x+1|的圖象即得：　x(1+√5)/2.

熱心網(wǎng)友

由巳知,將右邊換底得LOg1/2｜x｜＜LOg1/2｜x+1｜/Log1/2(1/4),化簡(jiǎn)為:Log1/2｜x｜＜1/2Log1/2｜x+1｜,即Log1/2｜x｜＜Log1/2√｜x+1｜,所以,｜x｜＞√｜x+1｜,兩邊平方:x平方＞｜x+1｜(1)當(dāng)x＜-1,x平方＞-x-1,即x平方+x+1＞0,成立,所以x＜-1是原不等式的解(2)當(dāng)x≥-1,x平方≥x+1,即x平方-x-1≥0,解得x≤(1-√5)/2或x≥(1+√5)/2,但x≥-1,故解集為-1≤x≤(1-√5)或x≥(1+√5)/2綜上,原不等式解集為x≤(1-√5)或x≥(1+√5)/2

熱心網(wǎng)友

㏒1/2|x|< ㏒1/4|x+1|等價(jià)于(即不等式右邊底數(shù)與真數(shù)同時(shí)開算術(shù)平方根)㏒1/2|x|< ㏒1/2√(|x+1|)所以|x|＞√(|x+1|)x^2＞|x+1|x+1≥0時(shí),x^2＞x+1,x^2-x-1＞0,x＞(1+√5)/2,或-1≤x＜(1-√5)/2或x+1≤0時(shí)x^2＞-(x+1),x^2+x+1＞0,△＜0,x∈R所以不等式的解是x＞(1+√5)/2,或-1≤x＜(1-√5)/2