n uchun yechish
n = \frac{6 \sqrt{6} + 9}{5} \approx 4,739387691
Baham ko'rish
Klipbordga nusxa olish
n=\left(n+3\right)\sqrt{\frac{3}{8}}
n qiymati -3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n+3 ga ko'paytirish.
n=\left(n+3\right)\times \frac{\sqrt{3}}{\sqrt{8}}
\sqrt{\frac{3}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{3}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.
n=\left(n+3\right)\times \frac{\sqrt{3}}{2\sqrt{2}}
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=\left(n+3\right)\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}
\frac{\sqrt{3}}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.
n=\left(n+3\right)\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}
\sqrt{2} kvadrati – 2.
n=\left(n+3\right)\times \frac{\sqrt{6}}{2\times 2}
\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.
n=\left(n+3\right)\times \frac{\sqrt{6}}{4}
4 hosil qilish uchun 2 va 2 ni ko'paytirish.
n=\frac{\left(n+3\right)\sqrt{6}}{4}
\left(n+3\right)\times \frac{\sqrt{6}}{4} ni yagona kasrga aylantiring.
n=\frac{n\sqrt{6}+3\sqrt{6}}{4}
n+3 ga \sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
n-\frac{n\sqrt{6}+3\sqrt{6}}{4}=0
Ikkala tarafdan \frac{n\sqrt{6}+3\sqrt{6}}{4} ni ayirish.
4n-\left(n\sqrt{6}+3\sqrt{6}\right)=0
Tenglamaning ikkala tarafini 4 ga ko'paytirish.
4n-n\sqrt{6}-3\sqrt{6}=0
n\sqrt{6}+3\sqrt{6} teskarisini topish uchun har birining teskarisini toping.
4n-n\sqrt{6}=3\sqrt{6}
3\sqrt{6} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.
\left(4-\sqrt{6}\right)n=3\sqrt{6}
n'ga ega bo'lgan barcha shartlarni birlashtirish.
\frac{\left(4-\sqrt{6}\right)n}{4-\sqrt{6}}=\frac{3\sqrt{6}}{4-\sqrt{6}}
Ikki tarafini 4-\sqrt{6} ga bo‘ling.
n=\frac{3\sqrt{6}}{4-\sqrt{6}}
4-\sqrt{6} ga bo'lish 4-\sqrt{6} ga ko'paytirishni bekor qiladi.
n=\frac{6\sqrt{6}+9}{5}
3\sqrt{6} ni 4-\sqrt{6} ga bo'lish.
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