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

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

n uchun yechish

$$n=\sqrt{10}+1\approx 4,16227766$$

$$n=1-\sqrt{10}\approx -2,16227766$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3n^{3} ga, n^{3},3n^{2} ning eng kichik karralisiga ko‘paytiring.

$$3\times 3=n\left(n-4\right)+n\times 2$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$9=n\left(n-4\right)+n\times 2$$

n ga n-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-2n ni olish uchun -4n va n\times 2 ni birlashtirish.

$$9=n^{2}-2n$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$n^{2}-2n=9$$

Ikkala tarafdan 9 ni ayirish.

$$n^{2}-2n-9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -9 ni c bilan almashtiring.

$$n=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-9\right)}}{2}$$

-2 kvadratini chiqarish.

$$n=\frac{-\left(-2\right)±\sqrt{4-4\left(-9\right)}}{2}$$

-4 ni -9 marotabaga ko'paytirish.

$$n=\frac{-\left(-2\right)±\sqrt{4+36}}{2}$$

4 ni 36 ga qo'shish.

$$n=\frac{-\left(-2\right)±\sqrt{40}}{2}$$

40 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-2\right)±2\sqrt{10}}{2}$$

-2 ning teskarisi 2 ga teng.

$$n=\frac{2±2\sqrt{10}}{2}$$

n=\frac{2±2\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{10} ga qo'shish.

$$n=\frac{2\sqrt{10}+2}{2}$$

2+2\sqrt{10} ni 2 ga bo'lish.

$$n=\sqrt{10}+1$$

n=\frac{2±2\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{10} ni ayirish.

$$n=\frac{2-2\sqrt{10}}{2}$$

2-2\sqrt{10} ni 2 ga bo'lish.

$$n=1-\sqrt{10}$$

Tenglama yechildi.

$$n=\sqrt{10}+1 n=1-\sqrt{10}$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3n^{3} ga, n^{3},3n^{2} ning eng kichik karralisiga ko‘paytiring.

$$3\times 3=n\left(n-4\right)+n\times 2$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$9=n\left(n-4\right)+n\times 2$$

n ga n-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-2n ni olish uchun -4n va n\times 2 ni birlashtirish.

$$9=n^{2}-2n$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$n^{2}-2n=9$$

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

$$n^{2}-2n+1=9+1$$

9 ni 1 ga qo'shish.

$$n^{2}-2n+1=10$$

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

$$\left(n-1\right)^{2}=10$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-1\right)^{2}}=\sqrt{10}$$

Qisqartirish.

$$n-1=\sqrt{10} n-1=-\sqrt{10}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$n=\sqrt{10}+1 n=1-\sqrt{10}$$