Question

Помогите решить систему уравнений:

14*49^x - 18*14^x - y = 0
y + 4^(x+1) = 0

Answer 1

у = 14*49^x - 18*14^x
y = -4^(x+1)
14*49^x - 18*14^x= -4^(x+1)
14*49^x - 18*14^x + 4^(x+1) = 0
14*(7²)^x - 18*(7*2)^x + (2²)^(x+1)=0
14*(7²)^x - 18*(7*2)^x + (2²)^x * (2²)^1 = 0
14*(7²)^x - 18*(7*2)^x + 4* (2²)^x = 0 | : (2²)^x ≠ 0
14*(7/2)^2x -18*(7/2)^x +4 = 0
(7/2)^x = t
14t² -18t +4 = 0
t = (9+-√81 - 56)/14 = (9 +-5)/14
t1 = 1                 t2 = 4/14 = 2/7
(7/)^x = 1           (7/2)^x = 2/7
x = 0                   x = -1