Докажите неравенство: (x^2+7)/корень из (x^2+6)>=2.

\[\frac{x^{2} + 7}{\sqrt{x^{2} + 6}} \geq 2,\ \ x^{2} + 7 > 0,\ \ \]

\[x^{2} + 6 > 0\]

\[\left( \frac{x^{2} + 7}{\sqrt{x^{2} + 6}} \right)^{2} \geq 4\]

\[\frac{x^{4} + 14x^{2} + 49 - 4x^{2} - 24}{x^{2} + 6} \geq 0\]

\[\frac{{(x}^{2} + 5)²}{x^{2} + 6} \geq 0\]

\[\left( x^{2} + 5 \right) \geq 0;\ \ \]

\[x^{2} + 6 > 0 \Longrightarrow верно.\]