+0  
 
0
35
2
avatar

For what real values of x is -4 < x^4 + 4x^2 < 5 satisfied? Express your answer in interval notation.

 Sep 28, 2021
 #1
avatar+47 
+1

We can narrow this expression to 0

Factor the expression into x^2(x^2+4). After setting x to 1, we can see that x must be less than 1 for the inequality to be satisfied.

Also, the expression cannot be less than 4 because x^2 cannot be negative. Setting x to 0 allows the expression to equal 4. 

 

But x can also be between -1 and 0 because of the rule with even exponents. So the final answer is -1

 

Hope that helpssmiley

 Sep 29, 2021
 #2
avatar+47 
+1

Sorry, my internet lagged out when I was posting this and it didn't save. Here's the right answer: -1 < x < 1

 Sep 29, 2021
edited by HedgieWedgie  Sep 29, 2021

18 Online Users