Question

Answer 1

\(x^2-2>-\sqrt{3}\)

=>\(x^2>2-\sqrt{3}\)

=>\(\left[{}\begin{matrix}x>\sqrt{2-\sqrt{3}}=\dfrac{1}{\sqrt{2}}\cdot\sqrt{4-2\sqrt{3}}=\dfrac{\sqrt{2}}{2}\left(\sqrt{3}-1\right)\\x< -\sqrt{2-\sqrt{3}}=-\dfrac{\sqrt{2}}{2}\left(\sqrt{3}-1\right)\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x>\dfrac{\sqrt{6}-\sqrt{2}}{2}\\x< \dfrac{-\sqrt{6}+\sqrt{2}}{2}\end{matrix}\right.\)

Answer 2

x² - 2 > -√3

⇔ x² > 2 - √3

⇔ x > √(2 - √3) hoặc x < -√(2-√3)