Решите 2^x - 8 * 2^-x = 7 - Все ответы

${2}^{x} - 8 \times {2}^{ - x} = 7 \\ {2}^{x} - \frac{8}{ {2}^{x} } = 7 \: \: \: |zamenim \: \: {2}^{x} = y \\ y - \frac{8}{y} = 7 \: \: \: | \times y \\ {y}^{2} - 8 = 7y \\ {y}^{2} - 7y - 8= 0 \\ d = {b}^{2} - 4ac = {7}^{2} - 4 \times ( - 8) = 49 +32 = 81 \\ y1 = \frac{ - b + \sqrt{d} }{2a} = \frac{7 + \sqrt{81} }{2} = \frac{7 + 9}{2} = \frac{16}{2} = 8 \\ y2 = \frac{ - b - \sqrt{d} }{2a} = \frac{7 - \sqrt{81} }{2} = \frac{7 - 9}{2} = \frac{ - 2}{2} = - 1 \\ - - - - - - - - \\ {2}^{x} = y1 \\ {2}^{x} = 8 \\ {2}^{x} = {2}^{3} \\ x1 = 3 \\ - - - - - - \\ {2}^{x} = y2 \\ {2}^{x} = - 1$
Ответ: х = 3