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  4. The solution set of (x-2)x3-6 x+8 > 1 is

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Q. The solution set of $(x-2)^{x^{3}-6 x+8} > 1$ is

Linear Inequalities

Solution:

Clearly $x > 2$.
Write the given inequality as
$\left(x^{2}-6 x+8\right) \log (x-2) > 0 \Leftrightarrow(x-2)(x-4) \log (x-2) > 0$
$\Leftrightarrow(x-4) \log (x-2) > 0 [\therefore x >2]$
image
From the sign scheme $x \in (2, 3) \cup (4, \infty)$