Question

$log_{0,2}(log_{2}(x^2-6x+5)) geq 0$

Answer 1

ОДЗ
x²-6x+5>0
x1+x2=6 u x1*x2=5⇒x1=1 U x2=5
x<1 u x>5
log(2)(x²-6x+5)>0⇒x²-6x+5>1
x²-6x+4>0
D=36-16=20
x1=(6-2√5)/2=3-√5 u x2=3+√5
x<3-√5 U x>3+√5
x∈(-∞;3-√5) U (3+√5;∞)
log(2)(x²-6x+5)≤1
x²-6x+5≤2
x²-6x+3≤0
D=36-12=24
x1=(6-2√6)/2=3-√6 U x2=3+√6
3-√6≤x≤3+√6
x∈[3-√6;3-√5) U (3+√5;3+√6]