(1)x/(x^2-8x+5)≥2(x-2x^2+16x-10)/(x^2-8x+5)≥0(2x^2-17x+10)/(x^2-8x+5)≤04-√11<x≤(17-√109)/4,或4+√11<x≤(17+√109)/4(2)x-1/x>0,(x^2-1)/x>0,(x-1)(x+1)/x>0-1<x<0,或x>1x-1/x<1,x<( 展开
(1)x/(x^2-8x+5)≥2(x-2x^2+16x-10)/(x^2-8x+5)≥0(2x^2-17x+10)/(x^2-8x+5)≤04-√11<x≤(17-√109)/4,或4+√11<x≤(17+√109)/4(2)x-1/x>0,(x^2-1)/x>0,(x-1)(x+1)/x>0-1<x<0,或x>1x-1/x<1,x<(1-√5)/2或0<x<(1+√5)/2所以-1<x<(1-√5)/2或1<x<(1+√5)/2(3)x^2-x-2>0,x>2或x<-12x-2>0,x>1x^2-x-2>2x-2x^2-3x>0,得x>3或x<0所以x>3(4)设t=3^x>0|t-1|+|t^2-3|>2当0<t<1时,不等式化为:1-t+3-t^2>2解得:t>1,或t<-2不符合0<t<1.当1≤t≤√3时,t-1+3-t^2>2解得:0<t<1不符合当t>√3时,t-1+t^2-3>2得t>2或t<-3所以t>2即3^x>2x>log<3>2(5)设t=log<2>x1/(1-t)≥1/(1+t)t/[(t+1)(t-1)]≤0t<-1或0≤t<1即log<2>x<-1,x<1/20≤log<2>x<1,1≤x<2所以x<1/2或1≤x<2 收起
