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Question

If log(x+1)(x22x)>0, then x

A
(12,0)(1+2,)
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B
(12,1+2){0}
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C
R{0}
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D
no solution
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Solution

The correct option is A (12,0)(1+2,)
x22x>0, x+1>0, & x+10,1x(,0)(2,), x>1, x1,0x(1,0)(2,)

logba>0a,b(0,1) or a,b(1,)

Case -1:
Let 0<x22x<1 and x+1(0,1)
0<x(x2)<1 and x(1,0)
x(x2)>0 and x(x2)<1
x(,0)(2,) and
x(x2)<1x22x1<0(x1)2<2x(12,1+2)
x(12,0) (1)

Case -2:
x22x>1 and x+1>1
x22x1>0 and x>0
x(1+2,) (2)

From (1)&(2),
x(12,0)(1+2,)

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