First slide

Introduction to linear inequalities

Question

$Number of integers satisfying (x^{2} - 4) \sqrt{x^{2} - 1} < 0 is$

Moderate

A

1
B

2
C

3
D

infinite

Solution

$(x^{2} - 4) \sqrt{x^{2} - 1} < 0$
$We must have x^{2} - 1 \geq 0$
$\begin{array}{l} or (x - 1) (x + 1) \geq 0 \\ or x \leq - 1 or x \geq 1 - - - - - (1) \\ Also (x^{2} - 4) \sqrt{x^{2} - 1} < 0 \\ \Rightarrow x^{2} - 4 < 0 \\ \Rightarrow - 2 < x < 2 - - - - - (2) \end{array}$
$From (i) and (ii) we have x \in (- 2, - 1] \cup [1, 2)$

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