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1i1kuz
@1i1kuz
July 2022
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Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2
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oganesbagoyan
Verified answer
task/25860145
--------------------
Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2
----
наверно : 6/|х-2|=|х-1|/ (х²-4)+28/ (х+2)
6/|х-2|=|х-1|/ (х+2)(x-2)+28/ (х+2) ОДЗ x ≠
±2 .
a) x < 1
-6/ (х -2)=-( х-1) / (х+2)(x-2)+28/
(х+ 2) ;
-6(x +2) = -x+1 +28(x-2)
33x = 43 ;
x = 43/33
→не удовлетворяет
.
----
б) 1
≤
x < 2
- 6/ (х-2)= ( х-1) / (х+2)(x-2)+28/
(х+2) ;
-6(x+2) = x -1 +28(x-2) ;
35x =45;
x = 9/7 .
----
в)
x > 2
6/ (х-2)= ( х-1) / (х+2)(x-2)+28/
(х+2) ;
6(x+2) = x
-1 +28(x-2) ;
23x =69 ;
x =3
ответ :
9/7
,
3
. * * *
1 2 /7 ; 3
* * *
1 votes
Thanks 1
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Answers & Comments
Verified answer
task/25860145--------------------
Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2
----
наверно : 6/|х-2|=|х-1|/ (х²-4)+28/ (х+2)
6/|х-2|=|х-1|/ (х+2)(x-2)+28/ (х+2) ОДЗ x ≠ ±2 .
a) x < 1
-6/ (х -2)=-( х-1) / (х+2)(x-2)+28/ (х+ 2) ;
-6(x +2) = -x+1 +28(x-2)
33x = 43 ;
x = 43/33 →не удовлетворяет .
----
б) 1≤ x < 2
- 6/ (х-2)= ( х-1) / (х+2)(x-2)+28/ (х+2) ;
-6(x+2) = x -1 +28(x-2) ;
35x =45;
x = 9/7 .
----
в) x > 2
6/ (х-2)= ( х-1) / (х+2)(x-2)+28/ (х+2) ;
6(x+2) = x -1 +28(x-2) ;
23x =69 ;
x =3
ответ : 9/7 , 3 . * * * 1 2 /7 ; 3 * * *