IMO Shortlist 1979 problem 6
Dodao/la:
arhiva2. travnja 2012. Find the real values of
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
for which the equation
![\sqrt{2p+ 1 - x^2} +\sqrt{3x + p + 4} = \sqrt{x^2 + 9x+ 3p + 9}](/media/m/7/e/a/7eace83dc2de4a551c35ef08e8632d31.png)
in
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
has exactly two real distinct roots.(
![\sqrt t](/media/m/5/5/b/55b0684606098b7bab23a17b5f9e766c.png)
means the positive square root of
![t](/media/m/7/f/6/7f630d3904cfcd77d22bd7938423df6c.png)
).
%V0
Find the real values of $p$ for which the equation
$$\sqrt{2p+ 1 - x^2} +\sqrt{3x + p + 4} = \sqrt{x^2 + 9x+ 3p + 9}$$
in $x$ has exactly two real distinct roots.($\sqrt t$ means the positive square root of $t$).
Izvor: Međunarodna matematička olimpijada, shortlist 1979