4. (a1-g10-9) $x+\frac{2}{x+\frac{2}{x+\frac{2}{\ldots}}}=6$, $x=?$. A) 1; B) $\frac12$; C) $\frac{17}{3}$; D) Hisoblab bo‘lmaydi.

Question

Вопрос: $Фото задания: 4. (a1-g10-9) $x+\frac{2}{x+\frac{2}{x+\frac{2}{\ldots}}}=6$, $x=?$. A) 1; B) $\frac12$; C) $\frac{17}{3}$; D)…$ Фото задания

Accepted Answer

Takrorlanuvchi kasrli ifodani $T$ deb belgilaymiz. Shartga ko‘ra $T=6$, ichki takrorlanuvchi qism ham $T$ ga teng. Shuning uchun $T=x+\frac{2}{T}$.

$6=x+\frac{2}{6}=x+\frac13$, demak $x=6-\frac13=\frac{17}{3}$.

Javob: C) $\frac{17}{3}$.

4. (a1-g10-9) \(x+\frac{2}{x+\frac{2}{x+\frac{2}{\ldots}}}=6\), \(x=?\). A) 1; B) \(\frac12\); C) \(\frac{17}{3}\); D) Hisoblab bo‘lmaydi.