Question

Решите неравенство, пожалуйста

Answer 1

Ответ:

${4}^{x + 1} + 7 \times {2}^{x} - 2 > 0 \\ {4}^{x} \times 4 + 7 \times {2}^{x} - 2 > 0 \\ 4 \times {2}^{2x} + 7 \times {2}^{x} - 2 > 0\\ \\ {2}^{x} = t,t > 0 \\ 4 {t}^{2} + 7 t - 2 > 0 \\ D = 49 + 32 = 81 \\ t1 = \frac{ - 7 + 9}{8} = \frac{1}{4} \\ t2 = - 2 \\ \\ (t + 2)(t - \frac{1}{4} ) > 0 \\ t = - 2 < 0 = > \\ > = t > \frac{1}{4} \\ {2}^{x} > \frac{1}{4} \\ {2}^{x} > {2}^{ - 2} \\ x > - 2$