←Vrati se na zadatke1. ZadatakIzračunaj: 202120212019⋅202120212021⋅202120212023100010001⋅(2021202120212−4).\frac{202120212019 \cdot 202120212021 \cdot 202120212023}{100010001 \cdot (202120212021^2 - 4)}.100010001⋅(2021202120212−4)202120212019⋅202120212021⋅202120212023.RješenjeNeka je x=202120212021x = 202120212021x=202120212021. Tada brojevni izraz poprima oblik: (x−2)⋅x⋅(x+2)100010001⋅(x2−4)=x⋅(x2−4)100010001⋅(x2−4)=x100010001\frac{(x - 2) \cdot x \cdot (x + 2)}{100010001 \cdot (x^2 - 4)} = \frac{x \cdot (x^2 - 4)}{100010001 \cdot (x^2 - 4)} = \frac{x}{100010001}100010001⋅(x2−4)(x−2)⋅x⋅(x+2)=100010001⋅(x2−4)x⋅(x2−4)=100010001x (uočimo da je 202120212021=2021⋅108+2021⋅104+2021=2021⋅100010001202120212021 = 2021 \cdot 10^8 + 2021 \cdot 10^4 + 2021 = 2021 \cdot 100010001202120212021=2021⋅108+2021⋅104+2021=2021⋅100010001) =2021⋅100010001100010001= \frac{2021 \cdot 100010001}{100010001}=1000100012021⋅100010001 =2021= 2021=2021