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  4. The solution of the inequality |x2 - 4x| < 5 is

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Q. The solution of the inequality $ |x^2 - 4x| < 5 $ is

AMUAMU 2018

Solution:

We have,
$| x^2 - 4x| < 5$
$\therefore -5 < x^2 - 4x < 5$
Case I $x^2 - 4x < 5$
$\Rightarrow x^2 - 4x-5 , 0$
$\Rightarrow (x - 5)(x + 1) < 0$
$ \Rightarrow x \in (-1, 5)$
Case II $ x^2 - 4x > - 5 ... (i)$
which is true $\forall x \in R$
$\Rightarrow x \in ( -\infty, \infty) ....$ (ii)
From Eqn. (i) and (ii),
$x \in(-1,5)$