Question 404494: Solve the inequality. Express the solution using interval notation.
x4 - 32x2 - 144 > 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve the inequality. Express the solution using interval notation.
x4 - 32x2 - 144 > 0
..
Factor to find critical points
x^4-32x^2-144=0
(x^2-36)(x^2+4)=0
x^2-36=0
(x+6)(x-6)=)
x=-6,x=6
x^2+4=0
x=+-sqrt(-4)= +-2i (2imaginary roots)
If you draw the critical points on the real number line, you will see there three intervals to consider,(-infinity,-6),(-6,6), and (6,infinity). Since f(x) is required to be >0 or positive, only the intervals where f(x)is positive, meet the requirement. You will find that the middle interval is negative and both intervals on either side are positive.
ans:
(-infinity,-6)union(6,+infinity)
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