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For what real values of x is -4 < x^4 + 4x^2 < 21 + 8x^2 satisfied?

 Jul 19, 2022
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x^4  + 4x^2   >  -4

 

x^4 + 4x^2  + 4 >  0

 

(x^2 + 2)^2  > 0

 

all  x values make this true

 

x^4 + 4x^2 < 21 + 8x^2

 

x^4 - 4x^2 - 21 <  0

 

(x^2 -7) ( x^2 + 3) <  0

 

The  interval   ( -sqrt 7  . sqrt 7 )  makes this true...and this  is the solution

 

 

cool cool cool

 Jul 19, 2022

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