9=n-4/3n^2+2/3n^2 eching

$$9 = \frac{ n-4 }{ 3 { n }^{ 2 } } + \frac{ 2 }{ 3 { n }^{ 2 } }$$

n uchun yechish

$$n=\frac{1+\sqrt{215}i}{54}\approx 0,018518519+0,271534783i$$

$$n=\frac{-\sqrt{215}i+1}{54}\approx 0,018518519-0,271534783i$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3n^{2} ga ko'paytirish.

$$27n^{2}=n-4+2$$

-2 olish uchun -4 va 2'ni qo'shing.

$$27n^{2}=n-2$$

Ikkala tarafdan n ni ayirish.

$$27n^{2}-n=-2$$

2 ni ikki tarafga qo’shing.

$$27n^{2}-n+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 27 ni a, -1 ni b va 2 ni c bilan almashtiring.

$$n=\frac{-\left(-1\right)±\sqrt{1-4\times 27\times 2}}{2\times 27}$$

-4 ni 27 marotabaga ko'paytirish.

$$n=\frac{-\left(-1\right)±\sqrt{1-108\times 2}}{2\times 27}$$

-108 ni 2 marotabaga ko'paytirish.

$$n=\frac{-\left(-1\right)±\sqrt{1-216}}{2\times 27}$$

1 ni -216 ga qo'shish.

$$n=\frac{-\left(-1\right)±\sqrt{-215}}{2\times 27}$$

-215 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-1\right)±\sqrt{215}i}{2\times 27}$$

-1 ning teskarisi 1 ga teng.

$$n=\frac{1±\sqrt{215}i}{2\times 27}$$

2 ni 27 marotabaga ko'paytirish.

$$n=\frac{1±\sqrt{215}i}{54}$$

n=\frac{1±\sqrt{215}i}{54} tenglamasini yeching, bunda ± musbat. 1 ni i\sqrt{215} ga qo'shish.

$$n=\frac{1+\sqrt{215}i}{54}$$

n=\frac{1±\sqrt{215}i}{54} tenglamasini yeching, bunda ± manfiy. 1 dan i\sqrt{215} ni ayirish.

$$n=\frac{-\sqrt{215}i+1}{54}$$

Tenglama yechildi.

$$n=\frac{1+\sqrt{215}i}{54} n=\frac{-\sqrt{215}i+1}{54}$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3n^{2} ga ko'paytirish.

$$27n^{2}=n-4+2$$

-2 olish uchun -4 va 2'ni qo'shing.

$$27n^{2}=n-2$$

Ikkala tarafdan n ni ayirish.

$$27n^{2}-n=-2$$

Ikki tarafini 27 ga bo‘ling.

$$\frac{27n^{2}-n}{27}=-\frac{2}{27}$$

27 ga bo'lish 27 ga ko'paytirishni bekor qiladi.

$$n^{2}-\frac{1}{27}n=-\frac{2}{27}$$

-\frac{1}{27} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{54} olish uchun. Keyin, -\frac{1}{54} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-\frac{1}{27}n+\left(-\frac{1}{54}\right)^{2}=-\frac{2}{27}+\left(-\frac{1}{54}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{54} kvadratini chiqarish.

$$n^{2}-\frac{1}{27}n+\frac{1}{2916}=-\frac{2}{27}+\frac{1}{2916}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{2}{27} ni \frac{1}{2916} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$n^{2}-\frac{1}{27}n+\frac{1}{2916}=-\frac{215}{2916}$$

n^{2}-\frac{1}{27}n+\frac{1}{2916} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-\frac{1}{54}\right)^{2}=-\frac{215}{2916}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{1}{54}\right)^{2}}=\sqrt{-\frac{215}{2916}}$$

Qisqartirish.

$$n-\frac{1}{54}=\frac{\sqrt{215}i}{54} n-\frac{1}{54}=-\frac{\sqrt{215}i}{54}$$

\frac{1}{54} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{1+\sqrt{215}i}{54} n=\frac{-\sqrt{215}i+1}{54}$$