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Please, can anyone solve this?

 

Solve the inequality x^3 - 4x < 0.

 May 5, 2020
 #1
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x^3 - 4x  <  0

 

x ( x^2 - 4)  < 0

 

x (x - 2) (x + 2)<  0      (1)

 

We  have  4  possible  intervals  that  might work

 

(-inf, -2)  or  (-2, 0)   or (0, 2)  or  ( 2, inf)

 

Note  that if 

x = -3   then the terms in (1)  have the signs  (-)(-)(-)  =  -   so true for this interval

x = -1  then the terms in (1)  have the signs  ( -)(-))+)  = +   so not true for this interval

x = 1     then the signs are  (+)(-)(+)  = -     so true for this interval

x =3      the signs are  (+) (+)(+)  = +    so  not true for this interva;

 

So.....the solution intevals  are  ( -inf, -2) U ( 0, 2)

 

See the graph here to confirm this :   https://www.desmos.com/calculator/vyj5pxzrj5

 

cool cool cool

 May 5, 2020

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