# Iminyaka emibili yabantu ababili1017

Cabanga ngabantu ababili $$A$$ no $$B$$ abangazalwanga ngosuku olufanayo futhi $$A$$ bancane kuno $$B$$ . Khombisa ukuthi kunemilaza emibili yeminyaka ncamashi $$a,b \in \mathbb{N}$$ , esebenza kuyo: $$2\cdot a = b$$ . Siqale ukusetha $$d \in \mathbb{R}^+$$ njengomehluko wobudala phakathi kuka $$A$$ no $$B$$ ekuzalweni kwe $$A$$ nge $$d = d_0 + d_1$$ , $$d_0 \in \mathbb{N}_0, d_1 \in \mathbb{R}, d_1 \in [0;1[$$ . Manje sibheka iphuzu lokuphikisana nesikhathi $$x \in \mathbb{R}^+$$ ngemuva kokuzalwa kwe- $$A$$ nge $$x = x_0 + x_1$$ , $$x_0 \in \mathbb{N}_0, x_1 \in \mathbb{R}, x_1 \in [0;1[$$ .

Ngalesi sikhathi ngesikhathi, ngencazelo, $$a = \lfloor x \rfloor$$ kanye $$b = \lfloor x+d \rfloor$$ . Manje sinquma konke $$x$$ okuphethe:

$$2 \lfloor x \rfloor = \lfloor x+d \rfloor \Leftrightarrow 2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor$$

Icala lokuqala: $$0 \leq x_1 + d_1 < 1$$:

Ngemuva kwalokho i- $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 \Leftrightarrow x_0 = d_0.$$

Lokhu kusho ukuthi $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + x_1 \rfloor = d_0$$ futhi $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ lokuqala lobudala $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ .

Icala lesibili: $$1 \leq x_1 + d_1 < 2$$:

Ngemuva kwalokho i- $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 + 1 \Leftrightarrow x_0 = d_0 + 1.$$

Lokhu kusho ukuthi $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + 1 + x_1 \rfloor = d_0 + 1$$ futhi $$b = \lfloor x+d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + 1 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor = 2 d_0 + 2$$ lesibili leminyaka eliyifunayo.

Ngokuqondile, lokhu kusho, ngokwesibonelo: Uma umama wakho wakubeletha eneminyaka $$20$$ , uneminyaka ephindwe kabili yobudala bakho eminyakeni engu - $$40$$ kanye $$42$$ . Kuyathakazelisa futhi uma ngabe $$n$$ izikhathi ezindala kunalezi: Lapha $$n \in \mathbb{N}$$ ngokungafanele futhi sithola $$x_0 = \frac{d_0}{n-1} \in \mathbb{N} \Leftrightarrow d_0 = k (n-1)$$ . Lokhu kusebenza ngqo lapho umehluko weminyaka ophelele $$\lfloor d \rfloor = d_0$$ kwe- $$n-1$$ , isb. Esimweni esingenhla unyoko uneminyaka $$24$$ $$6$$ iphinda iminyaka yakho.

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