Log_(2-5x) 3+log_(2-5x)2 ≤ 1/log₆(6x²-6x+1) ОДЗ 2-5х>0 x< 2/5
(6x²-6x+1) ≠1
Log_(2-5x) 3*2≤1/log₆(6x²-6x+1) 6x²-6x ≠0
6x(x-1)≠0
Log_(2-5x) 6 ≤ 1 /log₆(6x²-6x+1) х≠0 .х≠1
(6x²-6x+1) >0
1/ Log₆(2-5x) ≤ 1 /log₆(6x²-6x+1) D=36-24=12 √D=2√3
x₁= (6+2√3)/12= 1/2 +(√3)/6 ≈0,79
1/ Log₆(2-5x) ≤ 1 /log₆(6x²-6x+1) x₂ =(6- 2√3)/12 = 1/2- (√3)/6≈0,21
Log₆(2-5x) ≥ log₆(6x²-6x+1)
+ - +
(2-5x) ≥ (6x²-6x+1) ------∅--------0,21-----------0,79--------∅---------
6x²-6x+1 -2+5х ≤0 0 1
6х² -х-1≤0
x∉(-∞;0)∪(0 ;0,21)∪(0,79; +∞)
D=1+24=25 √D=5
x₁=(1+5)/12=1/2
х₂=(1-5)/12= - 1/3
+ - +
------------------ -1/3 ------------- 1/2 -------------------------
х [-1/3 ; 1/2] ,
с учетом ОДЗ х∈ [-1/3 ; 0)∪(0;(1/2- (√3)/6)]