SOLUTION: Solve the following inequality. x^4>x^2

Algebra ->  Inequalities -> SOLUTION: Solve the following inequality. x^4>x^2      Log On


   

Question 912702: Solve the following inequality.
x^4>x^2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4%3Ex%5E2
x%5E4-x%5E2%3E0
x%5E2%28x%5E2-1%29%3E0
x%5E2%28x-1%29%28x%2B1%29%3E0
Three critical points : x=0,x=1,x=-1
Break up the number line into 4 regions,
Region 1 : x%3C-1
Region 2 : -1%3Cx%3C0
Region 3 : 0%3Cx%3C1
Region 4 : x%3E1
Pick a point in each region (not the endpoint) and test the inequality.
If the inequality is satisfied the region is part of the solution.
Region 1 : x=-2
4%28-3%29%28-1%29%3E0
12%3E0
True, part of the solution region.
Region 2 : x=-1%2F2
%281%2F4%29%28-3%2F2%29%281%2F2%29%3E0
-3%2F16%3E0
False.
Region 3 : x=1%2F2
%281%2F4%29%28-1%2F2%29%283%2F2%29%3E0
-3%2F16%3E0
False.
Region 4: x=2
4%281%29%283%29%3E0
12%3E0
True, part of the solution region.
Now put it all together,
(-infinity,-1)U(1,infinity)
.
.
.
graph%28300%2C300%2C-3%2C3%2C-1%2C3%2Cx%5E4%2Cx%5E2%29
.
.
.
x%5E4 in Red
x%5E2 in Green