Question

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

Answer 1

$64^x-17*8^x+8=0\8^{2x} - 17*8^x+8=0\8^x = t > 0\t^2 - 17t+8 = 0\D = 289 - 32 = 257\t = frac{17pmsqrt{257}}{2}\ 8^x = frac{17pmsqrt{257}}{2}\x = log_8 frac{17pmsqrt{257}}{2}\x_1+x_2 = log_8frac{(17+sqrt{257})(17-sqrt{257})}{4} = log_8frac{32}{4} = log_88 = 1\Answer: 1$