решите неравенство: ㏒²₂(x-1)-㏒₀,₅(x-1)>2. Created by TaNyuShKa3001. algebra-ru

решите неравенство: ㏒²₂(x-1)-㏒₀,₅(x-1)>2...

MizoriesKun 0,5=1/2=2⁻¹
㏒²₂(x-1)-㏒₀,₅(x-1)>2 ОДЗ х-1>0 x>1
㏒²₂(x-1)-( -1㏒₂(x-1))>2
㏒²₂(x-1)+ ㏒₂(x-1)-2 > 0 замена ㏒₂(x-1)=а
а²+а-2=0
D=1+8=9
a₁=(-1+3)/2=1 ㏒₂(x-1)=1 x-1=2¹ x=3
a₂=(-1-3)/2=-2 ㏒₂(x-1)=-2 x-1=2⁻² x-1=1/4 x=1.1/4
+ - +
-----1------1,25------------3------------------

х∈(1;1,25)∪(3;+∞)

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TaNyuShKa3001 спасибо))

MizoriesKun удачи))

goodknif 0,5=1/2=2⁻¹
㏒²₂(x-1)-㏒₀,₅(x-1)>2 ОДЗ х-1>0 x>1
㏒²₂(x-1)-( -1㏒₂(x-1))>2
㏒²₂(x-1)+ ㏒₂(x-1)-2 > 0 замена ㏒₂(x-1)=а
а²+а-2=0
D=1+8=9
a₁=(-1+3)/2=1 ㏒₂(x-1)=1 x-1=2¹ x=3
a₂=(-1-3)/2=-2 ㏒₂(x-1)=-2 x-1=2⁻² x-1=1/4 x=1.1/4

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