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

Question

The solution set of (x-2)x3-6 x+8 > 1 is (A) (2, ∞) (B) (2,3) ∪(4, ∞) (C) (4,5) ∪(5, ∞) (D) (2,3) ∪(4,5)

Tardigrade Admin · Accepted Answer

Clearly x > 2. Write the given inequality as (x2-6 x+8) log (x-2) > 0 Leftrightarrow(x-2)(x-4) log (x-2) > 0 Leftrightarrow(x-4) log (x-2) > 0 [∴ x >2] <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3635e91b027635ca431071437b030310-.png" /> From the sign scheme x ∈ (2, 3) ∪ (4, ∞)

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

$(2, \infty)$

$(2, 3) \cup (4, \infty)$

$(4, 5) \cup (5, \infty)$

$(2, 3) \cup (4, 5)$

Clearly $x > 2$ .
Write the given inequality as
$(x^{2} - 6 x + 8) lo g (x - 2) > 0 \Leftrightarrow (x - 2) (x - 4) lo g (x - 2) > 0$
$\Leftrightarrow (x - 4) lo g (x - 2) > 0 [∴ x > 2]$

From the sign scheme $x \in (2, 3) \cup (4, \infty)$

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

(2,∞)

(2,3)∪(4,∞)

(4,5)∪(5,∞)

(2,3)∪(4,5)