不等式(x^2-x+1)(x^2-x-1)＞0的解集是

显示全部楼层 · 2013-5-11 17:50:51

解：因为x^2-x+1=x^2-2*(1/2)x+1/4-1/4+1=(x-1/2)^2+3/4＞0所以原不等式解集就是x^2-x-1＞0的解集。x^2-x-1＞0x^2-2*(1/2)*x+1/4-1/4-1＞0（x-1/2)^2-(√5/2)^2＞0（x-1/2+√5/2)(x-1/2-√5/2)＞0x＞（√5-1）/2或x＜-（√5+1）/2...

千问 · 2013-5-11 17:50:51

因为(x^2-x+1)恒大于0，所以只需求得(x^2-x-1)>0即可。解得x>(1+√5)/2或x<-(1+√5)/2。...