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natasgavrilova
@natasgavrilova
July 2022
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Помогите решить два уравнения!!!
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MizoriesKun
㏒₅х+ ㏒₅х-4=1 ОДЗ х>0 , x-4>0
x>4
㏒₅х*(х-4)=㏒₅5
㏒₅х²-4x =㏒₅5
х²-4x =5
х²-4x -5=0
D=16+20=36
x=(4+6)/2=5
x=(4-6)/2=-1 не подходит под ОДЗ
Ответ : х=5
--------------------------------------------------------------------------------------------
2㏒₃х=2㏒ₓ3 +3
2㏒₃х=2/ ㏒₃х +3 ОДЗ х>0
2㏒₃х=2/ ㏒₃х +3 домножим почленно на ㏒₃х
2㏒²₃х= 2+3㏒₃х
2㏒²₃х-3㏒₃х-2 =0 ,замена ㏒₃х=а
2а²-3а-2=0
D=9+16=25
a=(3+5)/4=2 ㏒₃х=2
x=3²=9
a=(3-5)/4=-1/2 ㏒₃х=-1/2
x=3⁻¹/² =1/√3
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Answers & Comments
㏒₅х*(х-4)=㏒₅5
㏒₅х²-4x =㏒₅5
х²-4x =5
х²-4x -5=0
D=16+20=36
x=(4+6)/2=5
x=(4-6)/2=-1 не подходит под ОДЗ
Ответ : х=5
--------------------------------------------------------------------------------------------
2㏒₃х=2㏒ₓ3 +3
2㏒₃х=2/ ㏒₃х +3 ОДЗ х>0
2㏒₃х=2/ ㏒₃х +3 домножим почленно на ㏒₃х
2㏒²₃х= 2+3㏒₃х
2㏒²₃х-3㏒₃х-2 =0 ,замена ㏒₃х=а
2а²-3а-2=0
D=9+16=25
a=(3+5)/4=2 ㏒₃х=2 x=3²=9
a=(3-5)/4=-1/2 ㏒₃х=-1/2 x=3⁻¹/² =1/√3