Иррациональные неравенства
§
\[\sqrt {f\left( x \right)} > g\left( x \right) \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
f\left( x \right) > {g^2}\left( x \right) \hfill \\
g\left( x \right) \geqslant 0 \hfill \\
\end{array} \right. \hfill \\
\left\{ \begin{array}{l}
f\left( x \right) \geqslant 0 \hfill \\
g\left( x \right) < 0 \hfill \\
\end{array} \right. \hfill \\
\end{array} \right.\]§
\[\sqrt {f\left( x \right)} < g\left( x \right) \Leftrightarrow \left\{ \begin{array}{l}
f\left( x \right) < {g^2}\left( x \right) \hfill \\
g\left( x \right) > 0 \hfill \\
f\left( x \right) \geqslant 0 \hfill \\
\end{array} \right.\]