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annianniclass
@annianniclass
July 2022
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Решить уравнение:
Lg(x-3)+Lg(x-2)=1-Lg5
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MizoriesKun
Verified answer
Lg(x-3)+Lg(x-2)=1-Lg5 ОДЗ х-2>0 x>2 , х-3>0 ,
x>3
Lg(x-3)*(x-2)= Lg10-Lg5
Lg(x-3)*(x-2)= Lg10/5
Lg(x-3)*(x-2)= Lg2
(x-3)*(x-2)= 2
x²-3x-2x+6-2=0
x²-5x+4=0
D=25-16=9 √D=3
x₁=(5+3)/2=4
x₂=(5-3)/2=1 не подходит под ОДЗ
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Answers & Comments
Verified answer
Lg(x-3)+Lg(x-2)=1-Lg5 ОДЗ х-2>0 x>2 , х-3>0 ,x>3Lg(x-3)*(x-2)= Lg10-Lg5
Lg(x-3)*(x-2)= Lg10/5
Lg(x-3)*(x-2)= Lg2
(x-3)*(x-2)= 2
x²-3x-2x+6-2=0
x²-5x+4=0
D=25-16=9 √D=3
x₁=(5+3)/2=4
x₂=(5-3)/2=1 не подходит под ОДЗ