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

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

n uchun yechish

$$n=\frac{-18\sqrt{6}-81}{19}\approx -6,583727125$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

n qiymati -3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n+3 ga ko'paytirish.

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

\sqrt{\frac{3}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{3}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$n=3\times \frac{\sqrt{3}}{2\sqrt{2}}\left(n+3\right)$$

\frac{\sqrt{3}}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$n=3\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}\left(n+3\right)$$

\sqrt{2} kvadrati – 2.

$$n=3\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}\left(n+3\right)$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$n=3\times \frac{\sqrt{6}}{2\times 2}\left(n+3\right)$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$n=3\times \frac{\sqrt{6}}{4}\left(n+3\right)$$

3\times \frac{\sqrt{6}}{4} ni yagona kasrga aylantiring.

$$n=\frac{3\sqrt{6}}{4}\left(n+3\right)$$

\frac{3\sqrt{6}}{4}\left(n+3\right) ni yagona kasrga aylantiring.

$$n=\frac{3\sqrt{6}\left(n+3\right)}{4}$$

3\sqrt{6} ga n+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$n=\frac{3\sqrt{6}n+9\sqrt{6}}{4}$$

Ikkala tarafdan \frac{3\sqrt{6}n+9\sqrt{6}}{4} ni ayirish.

$$n-\frac{3\sqrt{6}n+9\sqrt{6}}{4}=0$$

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$4n-\left(3\sqrt{6}n+9\sqrt{6}\right)=0$$

3\sqrt{6}n+9\sqrt{6} teskarisini topish uchun har birining teskarisini toping.

$$4n-3\sqrt{6}n-9\sqrt{6}=0$$

9\sqrt{6} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$4n-3\sqrt{6}n=9\sqrt{6}$$

n'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4-3\sqrt{6}\right)n=9\sqrt{6}$$

Ikki tarafini 4-3\sqrt{6} ga bo‘ling.

$$\frac{\left(4-3\sqrt{6}\right)n}{4-3\sqrt{6}}=\frac{9\sqrt{6}}{4-3\sqrt{6}}$$

4-3\sqrt{6} ga bo'lish 4-3\sqrt{6} ga ko'paytirishni bekor qiladi.

$$n=\frac{9\sqrt{6}}{4-3\sqrt{6}}$$

9\sqrt{6} ni 4-3\sqrt{6} ga bo'lish.

$$n=\frac{-18\sqrt{6}-81}{19}$$