4*5^(2x) + 5*4^(2x) = 9*20^x
Разделим всё уравнение на 4^(2x)
4*(5/4)^(2x) - 9*(5/4)^x + 5 = 0
t = (5/4)^x
4t^2 - 9t + 5 = 0
t1 = (9 + 1)/8 = 5/4
t2 = (9 - 1)/8 = 1
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Verified answer
4*5^(2x) + 5*4^(2x) = 9*20^x
Разделим всё уравнение на 4^(2x)
4*(5/4)^(2x) - 9*(5/4)^x + 5 = 0
t = (5/4)^x
4t^2 - 9t + 5 = 0
t1 = (9 + 1)/8 = 5/4
t2 = (9 - 1)/8 = 1