For what real values of x is -4 < x^4 + 4x^2 < 21 + 8x^2 satisfied?
x^4 + 4x^2 > -4
x^4 + 4x^2 + 4 > 0
(x^2 + 2)^2 > 0
all x values make this true
x^4 + 4x^2 < 21 + 8x^2
x^4 - 4x^2 - 21 < 0
(x^2 -7) ( x^2 + 3) < 0
The interval ( -sqrt 7 . sqrt 7 ) makes this true...and this is the solution
