# difficult inequality to solve

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bk97 on 25 Jan 2017
Commented: Walter Roberson on 26 Jan 2017
abs((cos(x)+1/2*x^2)-1)*x^4)<=1/24, does anybody have any idea how to solve this on matlab or write down some possible codes?

Niels on 25 Jan 2017
Edited: Niels on 25 Jan 2017
since your function is even it is symmetric and it is monotone for x>0 or x<0
use fzero
>> f=@(x)((cos(x)+1./2.*x.^2)-1).*x.^4 - 1/24 % subtract the value to transform it into an issue of roots
>> solution=abs(fzero(f,0))
solution =
1.0042
>> range=[-solution solution]
range =
-1.0042 1.0042
bk97 on 26 Jan 2017
alright thank you for the code about complex value! So could you please tell me if the code with the abs that @Niels has written before does work correctly for real solutions? And what is the conclusion for that
Walter Roberson on 26 Jan 2017
The +/- -1.004205445912837 I show occurs when the imaginary component is 0. It is a higher precision version of the value that Niels posted. The code Niels posted is fine.