Answer
$(-∞, -2) U (-1, 1) U (2, ∞) $
Work Step by Step
$x^8 - 17x^4 + 16 > 0$
Find the zeros of the expression.
$(x^4 - 16) (x^4 - 1)$
$(x^2 - 4) (x^2 + 4) (x^2 - 1) (x^2 + 1)$
$(x+2)(x+1)(x-1)(x-2)(x^2 + 4)(x^2 + 1)$
$x = -2, -1, 1, 2$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -2) $(-)(-)(-)(-)(+)(+) = (+)$
(-2, -1) $(+)(-)(-)(-)(+)(+) = (-)$
(-1, 1) $(+)(+)(-)(-)(+)(+) = (+)$
(1, 2) $(+)(+)(+)(-)(+)(+) = (-)$
(2, ∞) $(+)(+)(+)(+)(+)(+) = (+)$
Thus the solution is $(-∞, -2) U (-1, 1) U (2, ∞) $
