Question

Решите неравенство _________________

Answer 1

ОДЗ: 5x - x² > 0
x(5 - x)> 0
x(x - 5) < 0
x∈ (0 ; 5)
$log _{ \frac{1}{4} }(5x- x^{2} )+ \sqrt{5} ^{log _{3}1 } \ \textless \ 0\\\\log _{ \frac{1}{4} }(5x- x^{2} )+ \sqrt{5} ^{0} \ \textless \ 0\\\\log _{ \frac{1}{4} } (5x- x^{2} )+1\ \textless \ 0\\\\log _{ \frac{1}{4} } (5x- x^{2} )\ \textless \ -1\\\\5x- x^{2} \ \textgreater \ 4\\\\- x^{2} +5x-4\ \textgreater \ 0\\\\ x^{2} -5x+4\ \textless \ 0\\\\(x-4)(x-1)\ \textless \ 0$
         +                      -                          +
__________₀____________₀______________
                       1                        4
x ∈ (1 ; 4)

Answer 2

Task/28555881
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