IMO Shortlist 1959 problem 2
Dodao/la:
arhiva2. travnja 2012. For what real values of
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
is
![\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=A](/media/m/e/f/e/efed5f580969e6217052723c63f7989d.png)
given
a)
![A=\sqrt{2}](/media/m/0/6/d/06d2745566afbc83c138419df43fffea.png)
;
b)
![A=1](/media/m/e/b/e/ebef60a2d69817cd6472e869f66a9c54.png)
;
c)
![A=2](/media/m/7/5/e/75ee4324d90bc5eabac43df26e6077e8.png)
,
where only non-negative real numbers are admitted for square roots?
%V0
For what real values of $x$ is $$\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=A$$ given
a) $A=\sqrt{2}$;
b) $A=1$;
c) $A=2$,
where only non-negative real numbers are admitted for square roots?
Izvor: Međunarodna matematička olimpijada, shortlist 1959