# Kaping pindho umure wong loro1017

Coba pikirake wong loro $$A$$ lan $$B$$ sing ora lair dina sing padha lan $$A$$ luwih enom tinimbang $$B$$ . Tampilake: Ana persis loro konstelasi umur $$a,b \in \mathbb{N}$$ , sing ditrapake: $$2\cdot a = b$$ . Kaping pisanan nyetel $$d \in \mathbb{R}^+$$ minangka bedane umur antara $$A$$ lan $$B$$ nalika lair $$A$$ karo $$d = d_0 + d_1$$ , $$d_0 \in \mathbb{N}_0, d_1 \in \mathbb{R}, d_1 \in [0;1[$$ . Saiki kita nimbang titik sewenang-wenang wektu $$x \in \mathbb{R}^+$$ sawise lair $$A$$ kanthi $$x = x_0 + x_1$$ , $$x_0 \in \mathbb{N}_0, x_1 \in \mathbb{R}, x_1 \in [0;1[$$ .

Ing wektu iki, miturut definisi, $$a = \lfloor x \rfloor$$ lan $$b = \lfloor x+d \rfloor$$ . Saiki kita nemtokake kabeh $$x$$ sing nyekel:

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

Kasus kaping 1: $$0 \leq x_1 + d_1 < 1$$:

Banjur $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 \Leftrightarrow x_0 = d_0.$$

Iki tegese $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + x_1 \rfloor = d_0$$ lan $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ umur pisanan sing $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ .

Kasus kaping 2: $$1 \leq x_1 + d_1 < 2$$:

Banjur $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 + 1 \Leftrightarrow x_0 = d_0 + 1.$$

Iki tegese $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + 1 + x_1 \rfloor = d_0 + 1$$ lan $$b = \lfloor x+d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + 1 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor = 2 d_0 + 2$$ konstelasi umur kaping loro sing dikarepake.

Khusus, tegese, kayata: Yen ibumu nglairake sampeyan nalika umur $$20$$ taun, umure umure kaping pindho kaping pindho umure $$40$$ lan $$42$$ taun. Sampeyan uga bakal narik kawigaten yen lan nalika dheweke wis $$n$$ umure luwih tuwa: Ing kene $$n \in \mathbb{N}$$ sewenang-wenang lan kita entuk $$x_0 = \frac{d_0}{n-1} \in \mathbb{N} \Leftrightarrow d_0 = k (n-1)$$ . Iki bisa digunakake persis nalika bedane umur ongko ongko $$\lfloor d \rfloor = d_0$$ pirang-pirang $$n-1$$ , kayata ing kasus ing ndhuwur ibune $$24$$ taun $$6$$ umur sampeyan.

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