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Question

Solution set of the inequality (x2)x26x+8>1, where x>2 is

A
(2,3)(4,)
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B
(2,)
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C
(3,4)(4,)
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D
(2,4)
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Solution

The correct option is A (2,3)(4,)
(x2)x26x+8>1
For x>2
(x26x+8)log10(x2)>0
(x2)(x4)log10(x2)>0

Case 1:
(x2)(x4)>0 and log10(x2)>0
x((,2)(4,))(3,)
x(4,) (1)

Case 2:
(x2)(x4)<0 and log10(x2)<0
x(2,4)(2,3)
x(2,3) (2)

Now, (1)(2)
x(2,3)(4,)

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