1/alpha-1=1/2pi eching

$$\frac { 1 } { \alpha - 1 } = \frac { 1 } { 2 \pi }$$

α uchun yechish

$$\alpha =2\pi +1\approx 7,283185307$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\alpha qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \alpha -1 ga ko'paytirish.

$$1=\frac{1}{2}\left(\alpha -1\right)\pi ^{-1}$$

\frac{1}{2} ga \alpha -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1=\left(\frac{1}{2}\alpha -\frac{1}{2}\right)\pi ^{-1}$$

\frac{1}{2}\alpha -\frac{1}{2} ga \pi ^{-1} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1=\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}=1$$

\frac{1}{2}\pi ^{-1} ni ikki tarafga qo’shing.

$$\frac{1}{2}\alpha \pi ^{-1}=1+\frac{1}{2}\pi ^{-1}$$

Shartlarni qayta saralash.

$$\frac{1}{2}\times \frac{1}{\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{1}{\pi } ga ko‘paytiring.

$$\frac{1}{2\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

\frac{1}{2\pi }\alpha ni yagona kasrga aylantiring.

$$\frac{\alpha }{2\pi }=\frac{1}{2}\times \frac{1}{\pi }+1$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{1}{\pi } ga ko‘paytiring.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+1$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{2\pi }{2\pi } marotabaga ko'paytirish.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+\frac{2\pi }{2\pi }$$

\frac{1}{2\pi } va \frac{2\pi }{2\pi } da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\alpha }{2\pi }=\frac{1+2\pi }{2\pi }$$

Tenglama standart shaklda.

$$\frac{1}{2\pi }\alpha =\frac{2\pi +1}{2\pi }$$

Ikki tarafini \frac{1}{2}\pi ^{-1} ga bo‘ling.

$$\frac{\frac{1}{2\pi }\alpha \times 2\pi }{1}=\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

\frac{1}{2}\pi ^{-1} ga bo'lish \frac{1}{2}\pi ^{-1} ga ko'paytirishni bekor qiladi.

$$\alpha =\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

\frac{1+2\pi }{2\pi } ni \frac{1}{2}\pi ^{-1} ga bo'lish.

$$\alpha =2\pi +1$$

\alpha qiymati 1 teng bo‘lmaydi.

$$\alpha =2\pi +1\text{, }\alpha \neq 1$$