2^(2*x)<0 (неравенство)

Укажите решение неравенства: 2^(2*x)<0 (множество решений неравенства)

Вы ввели

 2*x    
2    < 0

$$2^{2 x} < 0$$

Подробное решение

Дано неравенство:
$$2^{2 x} < 0$$
Чтобы решить это нер-во - надо сначала решить соотвествующее ур-ние:
$$2^{2 x} = 0$$
Решаем:
$$x_{1} = -25.0161482956$$
$$x_{2} = -59.0161482956$$
$$x_{3} = -89.0161482956$$
$$x_{4} = -85.0161482956$$
$$x_{5} = -41.0161482956$$
$$x_{6} = -95.0161482956$$
$$x_{7} = -67.0161482956$$
$$x_{8} = -21.0161482956$$
$$x_{9} = -27.0161482956$$
$$x_{10} = -39.0161482956$$
$$x_{11} = -103.016148296$$
$$x_{12} = -35.0161482956$$
$$x_{13} = -51.0161482956$$
$$x_{14} = -31.0161482956$$
$$x_{15} = -71.0161482956$$
$$x_{16} = -99.0161482956$$
$$x_{17} = -69.0161482956$$
$$x_{18} = -81.0161482956$$
$$x_{19} = -101.016148296$$
$$x_{20} = -87.0161482956$$
$$x_{21} = -115.016148296$$
$$x_{22} = -105.016148296$$
$$x_{23} = -45.0161482956$$
$$x_{24} = -65.0161482956$$
$$x_{25} = -111.016148296$$
$$x_{26} = -107.016148296$$
$$x_{27} = -83.0161482956$$
$$x_{28} = -73.0161482956$$
$$x_{29} = -53.0161482956$$
$$x_{30} = -79.0161482956$$
$$x_{31} = -93.0161482956$$
$$x_{32} = -29.0161482956$$
$$x_{33} = -97.0161482956$$
$$x_{34} = -33.0161482956$$
$$x_{35} = -55.0161482956$$
$$x_{36} = -57.0161482956$$
$$x_{37} = -77.0161482956$$
$$x_{38} = -113.016148296$$
$$x_{39} = -63.0161482956$$
$$x_{40} = -43.0161482956$$
$$x_{41} = -23.0161482956$$
$$x_{42} = -109.016148296$$
$$x_{43} = -61.0161482956$$
$$x_{44} = -75.0161482956$$
$$x_{45} = -91.0161482956$$
$$x_{46} = -49.0161482956$$
$$x_{47} = -37.0161482956$$
$$x_{48} = -47.0161482956$$
$$x_{1} = -25.0161482956$$
$$x_{2} = -59.0161482956$$
$$x_{3} = -89.0161482956$$
$$x_{4} = -85.0161482956$$
$$x_{5} = -41.0161482956$$
$$x_{6} = -95.0161482956$$
$$x_{7} = -67.0161482956$$
$$x_{8} = -21.0161482956$$
$$x_{9} = -27.0161482956$$
$$x_{10} = -39.0161482956$$
$$x_{11} = -103.016148296$$
$$x_{12} = -35.0161482956$$
$$x_{13} = -51.0161482956$$
$$x_{14} = -31.0161482956$$
$$x_{15} = -71.0161482956$$
$$x_{16} = -99.0161482956$$
$$x_{17} = -69.0161482956$$
$$x_{18} = -81.0161482956$$
$$x_{19} = -101.016148296$$
$$x_{20} = -87.0161482956$$
$$x_{21} = -115.016148296$$
$$x_{22} = -105.016148296$$
$$x_{23} = -45.0161482956$$
$$x_{24} = -65.0161482956$$
$$x_{25} = -111.016148296$$
$$x_{26} = -107.016148296$$
$$x_{27} = -83.0161482956$$
$$x_{28} = -73.0161482956$$
$$x_{29} = -53.0161482956$$
$$x_{30} = -79.0161482956$$
$$x_{31} = -93.0161482956$$
$$x_{32} = -29.0161482956$$
$$x_{33} = -97.0161482956$$
$$x_{34} = -33.0161482956$$
$$x_{35} = -55.0161482956$$
$$x_{36} = -57.0161482956$$
$$x_{37} = -77.0161482956$$
$$x_{38} = -113.016148296$$
$$x_{39} = -63.0161482956$$
$$x_{40} = -43.0161482956$$
$$x_{41} = -23.0161482956$$
$$x_{42} = -109.016148296$$
$$x_{43} = -61.0161482956$$
$$x_{44} = -75.0161482956$$
$$x_{45} = -91.0161482956$$
$$x_{46} = -49.0161482956$$
$$x_{47} = -37.0161482956$$
$$x_{48} = -47.0161482956$$
Данные корни
$$x_{21} = -115.016148296$$
$$x_{38} = -113.016148296$$
$$x_{25} = -111.016148296$$
$$x_{42} = -109.016148296$$
$$x_{26} = -107.016148296$$
$$x_{22} = -105.016148296$$
$$x_{11} = -103.016148296$$
$$x_{19} = -101.016148296$$
$$x_{16} = -99.0161482956$$
$$x_{33} = -97.0161482956$$
$$x_{6} = -95.0161482956$$
$$x_{31} = -93.0161482956$$
$$x_{45} = -91.0161482956$$
$$x_{3} = -89.0161482956$$
$$x_{20} = -87.0161482956$$
$$x_{4} = -85.0161482956$$
$$x_{27} = -83.0161482956$$
$$x_{18} = -81.0161482956$$
$$x_{30} = -79.0161482956$$
$$x_{37} = -77.0161482956$$
$$x_{44} = -75.0161482956$$
$$x_{28} = -73.0161482956$$
$$x_{15} = -71.0161482956$$
$$x_{17} = -69.0161482956$$
$$x_{7} = -67.0161482956$$
$$x_{24} = -65.0161482956$$
$$x_{39} = -63.0161482956$$
$$x_{43} = -61.0161482956$$
$$x_{2} = -59.0161482956$$
$$x_{36} = -57.0161482956$$
$$x_{35} = -55.0161482956$$
$$x_{29} = -53.0161482956$$
$$x_{13} = -51.0161482956$$
$$x_{46} = -49.0161482956$$
$$x_{48} = -47.0161482956$$
$$x_{23} = -45.0161482956$$
$$x_{40} = -43.0161482956$$
$$x_{5} = -41.0161482956$$
$$x_{10} = -39.0161482956$$
$$x_{47} = -37.0161482956$$
$$x_{12} = -35.0161482956$$
$$x_{34} = -33.0161482956$$
$$x_{14} = -31.0161482956$$
$$x_{32} = -29.0161482956$$
$$x_{9} = -27.0161482956$$
$$x_{1} = -25.0161482956$$
$$x_{41} = -23.0161482956$$
$$x_{8} = -21.0161482956$$
являются точками смены знака неравенства в решениях.
Сначала определимся со знаком до крайней левой точки:
$$x_{0} < x_{21}$$
Возьмём например точку
$$x_{0} = x_{21} - \frac{1}{10}$$
=
$$-115.116148296$$
=
$$-115.116148296$$
подставляем в выражение
$$2^{2 x} < 0$$
$$2^{-115.116148296 \cdot 2} < 0$$

4.93370019405691e-70 < 0

но

4.93370019405691e-70 > 0

Тогда
$$x < -115.016148296$$
не выполняется
значит одно из решений нашего неравенства будет при:
$$x > -115.016148296 \wedge x < -113.016148296$$

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Другие решения неравенства будем получать переходом на следующий полюс
и т.д.
Ответ:
$$x > -115.016148296 \wedge x < -113.016148296$$
$$x > -111.016148296 \wedge x < -109.016148296$$
$$x > -107.016148296 \wedge x < -105.016148296$$
$$x > -103.016148296 \wedge x < -101.016148296$$
$$x > -99.0161482956 \wedge x < -97.0161482956$$
$$x > -95.0161482956 \wedge x < -93.0161482956$$
$$x > -91.0161482956 \wedge x < -89.0161482956$$
$$x > -87.0161482956 \wedge x < -85.0161482956$$
$$x > -83.0161482956 \wedge x < -81.0161482956$$
$$x > -79.0161482956 \wedge x < -77.0161482956$$
$$x > -75.0161482956 \wedge x < -73.0161482956$$
$$x > -71.0161482956 \wedge x < -69.0161482956$$
$$x > -67.0161482956 \wedge x < -65.0161482956$$
$$x > -63.0161482956 \wedge x < -61.0161482956$$
$$x > -59.0161482956 \wedge x < -57.0161482956$$
$$x > -55.0161482956 \wedge x < -53.0161482956$$
$$x > -51.0161482956 \wedge x < -49.0161482956$$
$$x > -47.0161482956 \wedge x < -45.0161482956$$
$$x > -43.0161482956 \wedge x < -41.0161482956$$
$$x > -39.0161482956 \wedge x < -37.0161482956$$
$$x > -35.0161482956 \wedge x < -33.0161482956$$
$$x > -31.0161482956 \wedge x < -29.0161482956$$
$$x > -27.0161482956 \wedge x < -25.0161482956$$
$$x > -23.0161482956 \wedge x < -21.0161482956$$

Быстрый ответ

Данное неравенство не имеет решений