The correct option is D { x:x lt;2 or x gt;4 } x^2 6x + 8 gt; 0 ⇒ (x 4) (x 2) gt; 0 Ref. imageIf x lt; 2 (x 2) ( ...

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Applications (Word Problem)

Solve x 2 -...

Question

Solve $x^{2} - 6 x + 8 > 0$

{x : x < 2 o r x > 4}

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{x : x > 2 o r x > 4}

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{x : x < 2 o r x < 4}

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None of these

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Solution

The correct option is D ${x : x < 2 o r x > 4}$
$x^{2} - 6 x + 8 > 0$
$\Rightarrow (x - 4) (x - 2) > 0$
Ref. image
If $x < 2 (x - 2) (x - 4) > 0$
$(\begin{matrix} ∵ (x - 2) \cap (x - 4) h a s o d d p o w e r ∴ s i g n c h a n g e a t 2, 4 \end{matrix})$
$\Rightarrow x \in (- \infty, 2) \cup (4, \infty)$
i.e. $x < 2$ or $x > y$

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