Решите неравенство: 3^x - 2^(x+1) sqrt(2 * 9^x - 10 * 6^x + 2^(2x+3)).

Положим t = (3/2)^x . Тогда 3^x - 2^(x+1) sqrt(2 * 9^x - 10 * 6^x + 2^(2x+3)) t - 2 sqrt(2t^2 - 10t + 8) [arrayl cases t 2 2t^2 - 10t + 8 0 cases (t - 2)^2 2t^2 - 10t + 8 array. [arrayl cases t 2 (t - 1)(t - 4) 0 cases t^2 - 6t + 4 0 array. [arrayl t 1 t 3 + sqrt(5) array. x in (-inf, 0] U [_((3)/(2))(3 + sqrt(5)), +inf).

\( x \in (-\infty, 0] \cup [\log_{\frac{3}{2}}(3 + \sqrt{5}), +\infty) \)