Решите неравенство (log4(64-x^2))^2-5log4(64-x^2)+6≥0

Question

Решите неравенство
(log4(64-x^2))^2-5log4(64-x^2)+6≥0

Answer 1

64-x²>0
(8-x)(8+x)>0
x=8  x=-8
x∈(-8;8)
log(4)(64-x²)=a
a²-5a+6≥0
a1+a2=5 U a1*a2=6
a1=2 U a2=3
a≤2⇒log(4)(64-x²)≤2⇒64-x²≤16⇒48-x²≤0⇒(4√3-x)(4√3+x)≤0
x=4√3  x=-4√3
x≤-4√3 U x≥4√3
x∈(-8;-4√3] U [4√3;8)
a2≥3⇒log(4)(64-x²)≥3⇒64-x²≥64≥x²≤0⇒x=0
Ответ x∈(-8;-4√3] U [4√3;8) U {0}