两题高一不等式
1个回答

(1)

x/(x²-8x+15)≥2

x/(x²-8x+15)-2≥0

x/(x²-8x+15)-2(x²-8x+15)/(x²-8x+15)≥0

(-2x²+17x-30)/(x²-8x+15)≥0

(2x²-17x+30)/(x²-8x+15)≤0

(x-6)(2x-5)/(x-3)(x-5)≤0

(x-6)(2x-5)(x-3)(x-5)≤0且(x-3)(x-5)≠0

由穿针引线法知道5/2≤x<3或5<x≤6

(2)

a>0

ax²-(a+1)x+1<0

(ax-1)(x-1)<0

①0<a<1时

1/a>1

所以解集是1<x<1/a

②a=1时

1/a=1

解集是空集

③a>1时

1/a<1

所以解集是1/a<x<1

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