For what real values of x is -4 < x^4 + 4x^2 < 21satisfied? Express your answer in interval notation.
Split the inequality......
x^4 + 4x^2 > -4
x^4 + 4x^2 + 4 > 0 factor
(x^2 + 2) ( x^2 + 2) > 0
(x^2 + 2)^2 > 0 all real numbers will work here
Also
x^4 + 4x^2 < 21
x^4 + 4x^2 - 21 < 0 factor
(x^2 + 7) ( x^2 - 3) < 0
This will be true when -sqrt (3) < x < sqrt (3)
We must take the most restrictive interval....this is
x = (-sqrt (3) , sqrt (3) )