4^(х-1)+2^(х-2)-3/2≥0

Question

4^(х-1)+2^(х-2)-3/2≥0

Answer 1

4^x * 1/4 + 2^x * 1/4 - 3/2  ≥ 0
4^x + 2^x - 6 ≥ 0 

2^x = t
t^2 + t - 6 ≥ 0 
t^2 + t - 6 = 0 
D = 1 +  4*6 = 25
t1 = ( - 1 + 5)/2 = 2
t2 = ( - 1 -  5)/2 = - 3

2^x = 2
x = 1

2^x = - 3
нет решений

x ∈ [1; + ∞)