ПОМОГИТЕ, ПОЖАЛУЙСТА РЕШИТЬ НЕРАВЕНСТВО. Created by dearneverland. algebra-ru

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ПОМОГИТЕ, ПОЖАЛУЙСТА РЕШИТЬ НЕРАВЕНСТВО...

mmb1

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Log5 (25x)/(log5 (x) + 2)+(log5 (x) - 2)/log5 (25x) ≥ (6 - log5 (x⁴))/(log²5 (x) -4)
одз х>0 log5 (x)≠2 x≠25 log5 (x)≠-2 x≠1/25
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log5 (25x) = log5 25 + log5 (x) = 2 + log5 (x)
log5 (x⁴) = 4*log5 (x)
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log5 (x) = t
(t +2)/(t+2) + (t-2)/(t+2) ≥ (6 - 4t) / (t²-4)
(t +2 + t -2)/(t+2) - 2*(3 - 2t) / (t²-4) ≥0
2t/(t+2) - 2*(3 - 2t) / (t-2)(t+2) ≥0
( t²-2t - 3 + 2t) /(t-2)(t+2) ≥0
( t²-3 ) /(t-2)(t+2) ≥0
( t-√3 )(t+√3)/(t-2)(t+2) ≥0

++++++++ (-2) ----------- [-√3] +++++++++ [√3] ------------ (2) +++++++++
t < -2
log5 x < -2 x>0 x<1/25
t > 2
log5 x > 2 x> 25
-√3≤t≤√3
log5 x ≥ -√3
x≥ 5^(-√3)
log5 x ≤√3
x≤5^(√3)
x∈(0 ,1/25) U [ 5^(-√3), 5^(√3)] U ( 25. +∞)

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pozhalujsta srochno najdite tochku minimuma funkcii y 15x2 48x189lnx 63

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