1. 2 * 2^x - 4*2^(-x) = 7;
2^x = t > 0;
2 t - 4/t = 7;
2 t^2 - 7t - 4 = 0;
D = 49 + 32 = 81 = 9^2;
t1 = (7+9) / 4 = 4; ⇒ 2^x = 4 ; x = 2.
t2 =( 7-9) / 4 = - 1/2 < 0.нет решений
Ответ х = 2
2. 7*4^x - 9*14^x + 2*49^x = 0; /:14^x >0;
7* 4^x / 14^x - 9 * 14^x / 14^x + 2 * 49^x / 14^x = 0;
7 * (2/7)^x - 9 + 2 * (7/2)^x = 0;
(2/7)^x = t;
((7/2)^x = 1/t;
7 t - 9 + 2/t = 0;
7 t^2 - 9 t + 2 = 0;
t1 = 1; ⇒ (7/2) ^x = 1; x1 =0;
t2 = 2/7; ⇒ (7/2)^x = 2/7; x2 = - 1.
x1 + x2 = 0 + (-1) = -1.
Ответ сумма корней равна минус 1