1/c_{T}=1/2+1/9+1/2+frac{1}{6}+frac{1}{12} eching

$$\frac { 1 } { c _ { T } } = \frac { 1 } { 2 } + \frac { 1 } { 9 } + \frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 }$$

c_T uchun yechish

$$c_{T}=\frac{36}{49}\approx 0,734693878$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

c_{T} qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 36c_{T} ga, c_{T},2,9,6,12 ning eng kichik karralisiga ko‘paytiring.

$$36=36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

\frac{36}{2} hosil qilish uchun 36 va \frac{1}{2} ni ko'paytirish.

$$36=\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

18 ni olish uchun 36 ni 2 ga bo‘ling.

$$36=18c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

\frac{36}{9} hosil qilish uchun 36 va \frac{1}{9} ni ko'paytirish.

$$36=18c_{T}+\frac{36}{9}c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

4 ni olish uchun 36 ni 9 ga bo‘ling.

$$36=18c_{T}+4c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

22c_{T} ni olish uchun 18c_{T} va 4c_{T} ni birlashtirish.

$$36=22c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

\frac{36}{2} hosil qilish uchun 36 va \frac{1}{2} ni ko'paytirish.

$$36=22c_{T}+\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

18 ni olish uchun 36 ni 2 ga bo‘ling.

$$36=22c_{T}+18c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

40c_{T} ni olish uchun 22c_{T} va 18c_{T} ni birlashtirish.

$$36=40c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

\frac{36}{6} hosil qilish uchun 36 va \frac{1}{6} ni ko'paytirish.

$$36=40c_{T}+\frac{36}{6}c_{T}+36c_{T}\times \frac{1}{12}$$

6 ni olish uchun 36 ni 6 ga bo‘ling.

$$36=40c_{T}+6c_{T}+36c_{T}\times \frac{1}{12}$$

46c_{T} ni olish uchun 40c_{T} va 6c_{T} ni birlashtirish.

$$36=46c_{T}+36c_{T}\times \frac{1}{12}$$

\frac{36}{12} hosil qilish uchun 36 va \frac{1}{12} ni ko'paytirish.

$$36=46c_{T}+\frac{36}{12}c_{T}$$

3 ni olish uchun 36 ni 12 ga bo‘ling.

$$36=46c_{T}+3c_{T}$$

49c_{T} ni olish uchun 46c_{T} va 3c_{T} ni birlashtirish.

$$36=49c_{T}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$49c_{T}=36$$

Ikki tarafini 49 ga bo‘ling.

$$c_{T}=\frac{36}{49}$$