Dani su pozitivni realni brojevi
![a_1](/media/m/6/1/7/6173ac27c63013385bea9def9ff2b61e.png)
,
![b_1](/media/m/9/e/3/9e348a34fc0fba0d71fb1d1c29f7d07d.png)
,
![c_1](/media/m/b/1/2/b127d6ccf61d390fb57243f93d0a377c.png)
,
![a_2](/media/m/4/0/1/401f4cdfec59fba73ae32fa6769c72cb.png)
,
![b_2](/media/m/7/4/9/74927f26391a89d5597bd1cb934fcc14.png)
,
![c_2](/media/m/c/7/6/c7689d03ec24d521da90ae97b120d93d.png)
za koje vrijedi
![b_1^2 \leqslant 4a_1c_1](/media/m/a/e/e/aeec981bfd92d18d899c561232c9b15f.png)
i
![b_2^2\leqslant 4a_2c_2](/media/m/2/6/a/26acd0bd7d68c8589471f29c79f5c353.png)
.
Dokaži da vrijedi
%V0
Dani su pozitivni realni brojevi $a_1$, $b_1$, $c_1$, $a_2$, $b_2$, $c_2$ za koje vrijedi $b_1^2 \leqslant 4a_1c_1$ i $b_2^2\leqslant 4a_2c_2$.
Dokaži da vrijedi $$4(a_1+a_2+5)(c_1+c_2+1)>(b_1+b_2+2)^2.$$