5^(2x+4) - 25*5^(x+ 4) - 5^x + 25 ≤ 0
5^(2x) * 5^4 - 25*5^x*5^4 - 5^x + 25 ≤ 0
625 * 5^(2x) - 15625 * 5^x - 5^x + 25 ≤ 0
625 * 5^(2x) - 15626 * 5^x + 25 ≤ 0
5^(x) = t
625t^2 - 15626t + 25 = 0
D = 244109376 = 15624^2
t1 = ( 15626 + 15624)/1250 = 25
t2 = ( 15626 - 15624)/1250 = 2/1250 = 1/625
5^x = 25
5^x = 5^2
x = 2
5^x = 1/625
5^x = 5^(-4)
x = - 4
(x + 4)(x - 2) ≤ 0
x ∈ [ - 4; 2]
Ответ
x ∈ [ - 4; 2]