Решите неравенство, плиз
[tex] 4^{x} -2* 5^{2x}- 10^{x} \ \textgreater \ 0 [/tex]
[tex] 4^{x} -2* 5^{2x}- 10^{x} \ \textgreater \ 0 [/tex]
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Answers & Comments
4^x - 2*5^2x - 10^x > 0
2^(2x) - 2*5^2x - (2^x)*(5^x) > 0 делим на (5^2x)
(2/5)^(2x) - (2/5)^x - 2 > 0
(2/5)^x = t, t > 0
t² - t - 2 > 0
t² - t - 2 = 0
t₁ = - 1 не удовлетворяет условию t > 0
t₂ = 2
(2/5)^x > 2
log₂/₅ (2/5)^x > log₂/₅ 2
так как 0 < 2/5 <1
x < log₂/₅ 2