Question

решите неравенство 3/(2^(2-x^2)-1)^2-4/(2^(2-x^2)-1)+1>=0

Answer 1

2^(2-x²)-1=a
3/a²-4/a +1≥0
(3-4a+a²)/a²≥0
a²-4a+3=0
a1+a2=4 U a1*a2=3⇒a1=1 U a2=3
a²=0⇒a=0
         +          +               _                 +
------------(0)--------[1]-------------[3]-----------------
1)a<0 ⇒2^(2-x²)-1<0⇒2^(2-x²)<1⇒2-x²<0⇒x∈(-√2;√2)
2)0<2^(2-x²)-1≤1
{2^(2-x²)-1>0⇒2^(2-x²)>1⇒2-x²>0⇒x<-√2 U x>√2
{2^(2-x²)-1≤1⇒2^(2-x²)≤2⇒2-x²≤1⇒1-x²≤0⇒x≤-1 U x≥1
x∈(-∞;-√2) U (√2;∞)
3)a≥3⇒2^(2-x²)-1≥3⇒2^(2-x²)≥4⇒2-x²≥2⇒x²≤0⇒x=0
Ответ x∈ (-∞;-√2) U (-√2;√2) U (√2;∞)