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Concept of Inequality

Solve the fol...

Question

Solve the following inequality:
$| x - 6 | < x^{2} - 5 x + 9$

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Solution

$| x - 6 | < x^{2} - 5 x + 9$
$x - 6 > - (x^{2} - 5 x + 9)$ & $x - 6 < x^{2} - 5 x + 9$
$x^{2} - 4 x + 3 > 0$ and $x^{2} - 6 x + 15 > 0$
$(x - 3) (x - 1) > 0$ and $D < 0$
$x ϵ (- \infty, 1) \cup (3, \infty)$ and So, $x ϵ R$
So, $x ϵ (- \infty, 1) \cup (3, \infty)$

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