Решите неравенство:

25^ (x+1) - 29*10^x + 4^ (x+1) >=0

25^ (х+1) - 29*10^х+4^ (х+1) ≥0

25*25^х-29*10^х+4*4^х≥0; (:4^х>0)

25 * (25/4) ^х-29 * (10/4) ^х+4≥0

25 * (5/2) ^ (2 х) - 29 * (5/2) ^х+4≥0

(5/2) ^х=t>0

25t²-29t+4≥0

D=29²-400=841-400=441=21²

t = (29±21) / 50

t1=1; t2=8/50=4/25

t€ (-бес; 4/25]+[1; + бес)

1) (5/2) ^х≥1; х≥0

2) (5/2) ^х≤4/25

(5/2) ^х≤ (5/2) ^ (-2)

х≤-2

ответ х≥0; х≤-2