Question

Решите неравенство
$frac{45}{(4^{2-x^{2} } - 1)^2} - frac{18}{4^2-x^} -1} + 1 geq 0$

Answer 1

²ОДЗ
4^(2-x²)-1≠0
4^(2-x²)≠1
2-x²≠0
x²≠2
x≠-√2 U x≠√2
4^(2-x²)-1=a
45/a²-18/a+1≥0
45-18a+a²≥0
a1+a2=18 U a1*a2=45
a1=3 U a2=15
               +                  _                +
------------------[3]--------------[15]----------------
a≤3⇒4^(2-x²)≤3⇒2-x²≤log(4)3⇒(x-√(2-log(4)3))(x+√(2-log(4)3))≥0
x≤-√(2-log(4)3) U x≥√(2-log(4)3)
a≥15⇒4^(2-x²)≥15⇒2-x²≥log(4)15⇒(x-√(2-log(4)15))(x+√(2-log(4)15))≤0
-√(2-log(4)15)≤x≤√(2-log(4)15)