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Greatest Integer Function

Solve the fol...

Question

Solve the following inequalities.
$l o g_{1 / 2} (x^{2} + 2 x + 4) > - 2.$

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Solution

${log}_{1 / 2} (x^{2} + 2 x + 4) > - 2$

$⟹ x^{2} + 2 x + 4 < {(\frac{1}{2})}^{- 2} = 4$

$⟹ x^{2} + 2 x < 0$

$⟹ x (x + 2) < 0$

$⟹ x \in (- 2, 0)$

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