(0.81) ^{ x} \\ ({ \frac{9}{10} })^{ - \frac{ {x}^{2} - 45 }{2} } > (0.9) ^{2x} \\ - \frac{ {x}^{2} - 45}{2} > 2x \\ - {x}^{2} + 45 - 4x > 0 \\ {x}^{2} + 2x - 45 < 0 \\ {x}^{2} + 4x - 45 = 0 \\ d = 16 + 180 = 196 \\ x = \frac{ - 4 + 14}{2} = 5 \\ x = \frac{ - 4 - 14}{2} = - 9 \\ " alt="( \frac{ \sqrt{10} }{3}) ^{ {x}^{2} - 45} > (0.81) ^{ x} \\ ({ \frac{9}{10} })^{ - \frac{ {x}^{2} - 45 }{2} } > (0.9) ^{2x} \\ - \frac{ {x}^{2} - 45}{2} > 2x \\ - {x}^{2} + 45 - 4x > 0 \\ {x}^{2} + 2x - 45 < 0 \\ {x}^{2} + 4x - 45 = 0 \\ d = 16 + 180 = 196 \\ x = \frac{ - 4 + 14}{2} = 5 \\ x = \frac{ - 4 - 14}{2} = - 9 \\ " align="absmiddle" class="latex-formula">
Знаки: ____+++___(-9)___---___(5)____+++__> x
Ответ :(-∞;-9)U(5;+∞)