$w\left(x\right)=4x^3-4\sqrt{2}{x}^2-3x+3\sqrt{2}$  

Obliczamy pierwiastki wielomianu w:

$w\left(x\right)=0$  

$4x^3-4\sqrt{2}{x}^2-3x+3\sqrt{2}=0$  

$4x^2\left(x-\sqrt{2}\right)-3\left(x-\sqrt{2}\right)=0\mid :4$  

$x^2\left(x-\sqrt{2}\right)-\frac{3}{4}\left(x-\sqrt{2}\right)=0$  

$\left(x-\sqrt{2}\right)\left(x^2-\frac{3}{4}\right)=0$  

$\left(x-\sqrt{2}\right)\left(x-\frac{\sqrt{3}}{2}\right)\left(x+\frac{\sqrt{3}}{2}\right)=0$  

$x=\sqrt{2}\text{lub}x=\frac{\sqrt{3}}{2}\text{lub}x=-\frac{\sqrt{3}}{2}$  

---

Obliczamy S:

$S=\left|\sqrt{2}\right|+\left|\frac{\sqrt{3}}{2}\right|+\left|-\frac{\sqrt{3}}{2}\right|=\sqrt{2}+\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}=\sqrt{2}+\sqrt{3}\approx 1,41+1,73=3,14$  

---

Należy zakodować liczbę 314.