An algebra problem by A Former Brilliant Member

Algebra Level 4

$\large 2^{2x^2-10x+3}+6^{x^2-5x+1} \geq 3^{2x^2-10x+3}$

The set of values of $x$ for which above inequality holds is given by:

\left[-\infty,-\left(\frac{5+\sqrt{21}}{2}\right)\right]

\left[\frac{5-\sqrt{21}}{2},\frac{5+\sqrt{21}}{2}\right]

\left[-\frac{5+\sqrt{21}}{2},\frac{5+\sqrt{21}}{2}\right]

(-\infty ,\infty)