Log_6 (x² -5x) * Log_6 (7x² -x) - Log_6 x²(7x² -36x +5) +1 =0 ;
Log_6 (x² -5x) * Log_6 (7x² -x) - Log_6 (7x² -x)(x²-5x) +1 =0 ;
Log_6 (x² -5x) * Log_6 (7x² -x) - Log_6 (7x² -x) - Log_6 (x²-5x) + 1 =0 ;
(Log_6 (7x² -x) -1)*( Log_6 (x² -5x) -1) =0 ;
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ОДЗ: { x² -5x > 0 ; 7x² -x >0 ⇔ { x(x -5) > 0 ; 7x(x -1/7) >0 ⇒
x∈(-∞ ; 0) U (5 ;∞)
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[ Log_6 (7x² -x) =1 ; Log_6 (x² -5x) =1.
[ 7x² -x -6 =0 ; x² -5x -6 =0.⇔ [ x = -6/7 ; x =1 ; x = -1 ; x =6 .
x=1 ∉ ОДЗ.
ответ : { -1; - 6/7 ; 6 } .
* * * P.S 7x² -36x +5 =0 ⇒x₁ =1/7 ; x₂ =5⇒7x² -36x +5 =7(x -1/7)(x-5) =
(7x-1)(x-5) и x²(7x² -36x +5) = x(7x-1) *x(x-5) =( 7x²-x) *(x²-5x)* * *