Marinada '21

[lang=hr] Jednadžba $x^4 - 2x^3 - 3x^2 - 2x + 1 = 0$ ima dva realna rješenja. Veće od ta dva rješenja možemo napisati u obliku \[ x = \frac{a+\sqrt{b} + \sqrt{c + d\sqrt{b}} }{e} \] pri čemu su $a$, $b$, $c$, $d$ i $e$ prirodni brojevi, a dani izraz je do kraja skraćen i djelomično korjenovan. \\ Koliko iznosi $a + b + c + d + e$? [/lang] [lang=en] The equation $x^4 - 2x^3 - 3x^2 - 2x + 1 = 0$ has two real solutions. The larger solution can be expressed in the following way: \[ x = \frac{a+\sqrt{b} + \sqrt{c + d\sqrt{b}} }{e} \] where $a$, $b$, $c$, $d$ and $e$ are natural numbers and the expression above (fraction and radicals) is in simplest form. \\ Find $a + b + c + d + e$. [/lang]