+0  
 
+1
83
1
avatar+20 

For what real values of x is -4 < x^4 + 4x^2 < 21satisfied? Express your answer in interval notation.

 Mar 23, 2021
edited by Guest  Mar 23, 2021
 #1
avatar+121000 
+2

Split the inequality......

 

x^4 + 4x^2  >  -4

 

x^4 + 4x^2 + 4  >  0     factor

 

(x^2  + 2) ( x^2 + 2) > 0

 

(x^2 + 2)^2  >  0         all  real numbers will work here

 

Also

 

x^4 + 4x^2  <  21

 

x^4 + 4x^2  - 21 <  0     factor

 

(x^2 + 7) ( x^2 - 3)  <  0

 

This  will be true   when       -sqrt (3)  < x < sqrt (3)

 

We  must  take  the most restrictive  interval....this is

 

x =  (-sqrt (3)  , sqrt (3) )

 

cool cool cool

 Mar 23, 2021
edited by CPhill  Mar 23, 2021

15 Online Users

avatar