Log5^2 (25-x^2)-3log5(25-x^2)+2>=0

Question

Log5^2 (25-x^2)-3log5(25-x^2)+2>=0

Answer 1

ОДЗ  (5-x)(5+x)⇒x∈(-5;5)
log(5)(25-x²)=a
a²-3a+2≥0
a1+a2=3 U a1*a2=2⇒a1=1 U a2=2
a≤1⇒log(5)(25-x²)≤1⇒25-x²≤5⇒(20-x²)≤0⇒(2√5-x)(2√5+x)≤0⇒x≤-2√5 U x≥2√5
a≥2⇒log(5)(25-x²)≥2⇒25-x²≥25⇒x²≤0⇒x=0
x∈(-5;-2√5] U [2√5;5) U x=0