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已知a>2解不等式组 a(x-2)+1>0 (x-1)²>a(x-2)+1
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a(x-2)+1>0 x-2>-1/a x>2-1/a ∵a>2 ∴1/a<1/2 2-1/a>3/2 x>3/2
(x-1)²>a(x-2)+1 (x-1)²-a(x-2)-1>0 x²-2x+1-ax+2a-1>0 x²-(a+2)x+2a>0 (x-a)(x-2)>0
x-a>0 x-2>0 或x-a<0 x-2<0 ∵a>2 ∴x>2或x<2
(x-1)²>a(x-2)+1 (x-1)²-a(x-2)-1>0 x²-2x+1-ax+2a-1>0 x²-(a+2)x+2a>0 (x-a)(x-2)>0
x-a>0 x-2>0 或x-a<0 x-2<0 ∵a>2 ∴x>2或x<2
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