IMO Shortlist 1973 problem 11
Dodao/la:
arhiva2. travnja 2012. Determine the minimum value of
![a^{2} + b^{2}](/media/m/6/d/3/6d3d14b2df344553404ea47d410902c5.png)
when
![(a,b)](/media/m/e/2/6/e263229694cdbeb908488db2d0351f0a.png)
traverses all the pairs of real numbers for which the equation
![x^{4} + ax^{3} + bx^{2} + ax + 1 = 0](/media/m/4/4/6/446e0dd79037f065c9915ecc2536c5c7.png)
has at least one real root.
%V0
Determine the minimum value of $a^{2} + b^{2}$ when $(a,b)$ traverses all the pairs of real numbers for which the equation $$x^{4} + ax^{3} + bx^{2} + ax + 1 = 0$$ has at least one real root.
Izvor: Međunarodna matematička olimpijada, shortlist 1973