2+1/2+1{1+frac{1/2+frac{1{A}}}}=64/27 eching

$$2 + \frac { 1 } { 2 + \frac { 1 } { 1 + \frac { 1 } { 2 + \frac { 1 } { A } } } } = \frac { 64 } { 27 }$$

A uchun yechish

$$A=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2+\frac{1}{2+\frac{1}{1+\frac{1}{\frac{2A}{A}+\frac{1}{A}}}}=\frac{64}{27}$$

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

$$2+\frac{1}{2+\frac{1}{1+\frac{1}{\frac{2A+1}{A}}}}=\frac{64}{27}$$

A qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{2A+1}{A} ga bo'lish 1 ga k'paytirish \frac{2A+1}{A} ga qaytarish.

$$2+\frac{1}{2+\frac{1}{1+\frac{A}{2A+1}}}=\frac{64}{27}$$

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

$$2+\frac{1}{2+\frac{1}{\frac{2A+1}{2A+1}+\frac{A}{2A+1}}}=\frac{64}{27}$$

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

$$2+\frac{1}{2+\frac{1}{\frac{2A+1+A}{2A+1}}}=\frac{64}{27}$$

2A+1+A kabi iboralarga o‘xshab birlashtiring.

$$2+\frac{1}{2+\frac{1}{\frac{3A+1}{2A+1}}}=\frac{64}{27}$$

A qiymati -\frac{1}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{3A+1}{2A+1} ga bo'lish 1 ga k'paytirish \frac{3A+1}{2A+1} ga qaytarish.

$$2+\frac{1}{2+\frac{2A+1}{3A+1}}=\frac{64}{27}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{3A+1}{3A+1} marotabaga ko'paytirish.

$$2+\frac{1}{\frac{2\left(3A+1\right)}{3A+1}+\frac{2A+1}{3A+1}}=\frac{64}{27}$$

\frac{2\left(3A+1\right)}{3A+1} va \frac{2A+1}{3A+1} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$2+\frac{1}{\frac{2\left(3A+1\right)+2A+1}{3A+1}}=\frac{64}{27}$$

2\left(3A+1\right)+2A+1 ichidagi ko‘paytirishlarni bajaring.

$$2+\frac{1}{\frac{6A+2+2A+1}{3A+1}}=\frac{64}{27}$$

6A+2+2A+1 kabi iboralarga o‘xshab birlashtiring.

$$2+\frac{1}{\frac{8A+3}{3A+1}}=\frac{64}{27}$$

A qiymati -\frac{1}{3} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{8A+3}{3A+1} ga bo'lish 1 ga k'paytirish \frac{8A+3}{3A+1} ga qaytarish.

$$2+\frac{3A+1}{8A+3}=\frac{64}{27}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{8A+3}{8A+3} marotabaga ko'paytirish.

$$\frac{2\left(8A+3\right)}{8A+3}+\frac{3A+1}{8A+3}=\frac{64}{27}$$

\frac{2\left(8A+3\right)}{8A+3} va \frac{3A+1}{8A+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(8A+3\right)+3A+1}{8A+3}=\frac{64}{27}$$

2\left(8A+3\right)+3A+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{16A+6+3A+1}{8A+3}=\frac{64}{27}$$

16A+6+3A+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{19A+7}{8A+3}=\frac{64}{27}$$

A qiymati -\frac{3}{8} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 27\left(8A+3\right) ga, 8A+3,27 ning eng kichik karralisiga ko‘paytiring.

$$27\left(19A+7\right)=64\left(8A+3\right)$$

27 ga 19A+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$513A+189=64\left(8A+3\right)$$

64 ga 8A+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$513A+189=512A+192$$

Ikkala tarafdan 512A ni ayirish.

$$513A+189-512A=192$$

A ni olish uchun 513A va -512A ni birlashtirish.

$$A+189=192$$

Ikkala tarafdan 189 ni ayirish.

$$A=192-189$$

3 olish uchun 192 dan 189 ni ayirish.

$$A=3$$