Question

Найдите сумму корней уравнения :
64^x-17*8^x+8=0

Answer 1

$64^x-17*8^x+8=0\\8^{2x} - 17*8^x+8=0\\8^x = t > 0\\t^2 - 17t+8 = 0\\D = 289 - 32 = 257\\t = \frac{17\pm\sqrt{257}}{2}\\ 8^x = \frac{17\pm\sqrt{257}}{2}\\x = log_8 \frac{17\pm\sqrt{257}}{2}\\x_1+x_2 = log_8\frac{(17+\sqrt{257})(17-\sqrt{257})}{4} = log_8\frac{32}{4} = log_88 = 1\\Answer: 1$