n/3+n=frac{sqrt{3}}{8} eching

$$\frac{ n }{ 3+n } = \frac{ \sqrt{ 3 } }{ 8 }$$

n uchun yechish

$$n=\frac{24\sqrt{3}+9}{61}\approx 0,829003596$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$8n=\left(n+3\right)\sqrt{3}$$

n+3 ga \sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8n=n\sqrt{3}+3\sqrt{3}$$

Ikkala tarafdan n\sqrt{3} ni ayirish.

$$8n-n\sqrt{3}=3\sqrt{3}$$

Shartlarni qayta saralash.

$$-\sqrt{3}n+8n=3\sqrt{3}$$

n'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-\sqrt{3}+8\right)n=3\sqrt{3}$$

Tenglama standart shaklda.

$$\left(8-\sqrt{3}\right)n=3\sqrt{3}$$

Ikki tarafini -\sqrt{3}+8 ga bo‘ling.

$$\frac{\left(8-\sqrt{3}\right)n}{8-\sqrt{3}}=\frac{3\sqrt{3}}{8-\sqrt{3}}$$

-\sqrt{3}+8 ga bo'lish -\sqrt{3}+8 ga ko'paytirishni bekor qiladi.

$$n=\frac{3\sqrt{3}}{8-\sqrt{3}}$$

3\sqrt{3} ni -\sqrt{3}+8 ga bo'lish.

$$n=\frac{24\sqrt{3}+9}{61}$$