Question

решите неравенство! Срочно, пожалуйста!
$15 {}^{x {}^{2} - 9 } < 225 {}^{4x}$
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Answer 1

$\displaystyle\bf\\15^{x^{2} -9} < 225^{4x} \\\\\\15^{x^{2} -9} < (15^{2} )^{4x}\\\\\\15^{x^{2} -9} < 15^{8x}\\\\\\15 > 1 \ \ \ \Rightarrow \ \ \ x^{2} -9 < 8x\\\\\\x^{2} -8x-9 < 0\\\\\\(x+1)(x-9) < 0\\\\\\+ + + + + (-1) - - - - - (9) + + + + +$

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$\displaystyle\bf\\Otvet \ : \ x\in \ (-1 \ ; \ 9)$