Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2. Created by 1i1kuz. algebra-ru

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1i1kuz @1i1kuz

July 2022 1 25 Report

Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2

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oganesbagoyan

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task/25860145
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Решите уравнение: 6/|х-2|=|х-1|/х^2-4+28/х+2
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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 .
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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 .
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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 * * *

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