Найдите множество решений неравенства: (9x^2-4)(16-x^2)(2x^2+3)>0.

Ответ:

\[\left( 9x^{2} - 4 \right)\left( 16 - x^{2} \right)\left( 2x^{2} + 3 \right) > 0\]

\[2x^{2} + 3 > 0;\]

\[- 9\left( x^{2} - \frac{4}{9} \right)\left( x^{2} - 16 \right) > 0\]

\[\left( x + \frac{2}{3} \right)\left( x - \frac{2}{3} \right)(x + 4)(x - 4) < 0\]

\[(x + 4)\left( x + \frac{2}{3} \right)\left( x - \frac{2}{3} \right)(x - 4) < 0\]

\[- 4 < x < - \frac{2}{3};\ \ \frac{2}{3} < x < 4.\]