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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