n/n+1=3/5*n eching

$$\frac { n } { n + 1 } = \frac { 3 } { 5 } \cdot n$$

n uchun yechish

$$n=\frac{2}{3}\approx 0,666666667$$

$$n=0$$

Faktorlash qadamlari

n qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5\left(n+1\right) ga, n+1,5 ning eng kichik karralisiga ko‘paytiring.

$$5n=\frac{3}{5}n\times 5\left(n+1\right)$$

3 hosil qilish uchun \frac{3}{5} va 5 ni ko'paytirish.

$$5n=3n\left(n+1\right)$$

3n ga n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5n=3n^{2}+3n$$

Ikkala tarafdan 3n^{2} ni ayirish.

$$5n-3n^{2}=3n$$

Ikkala tarafdan 3n ni ayirish.

$$5n-3n^{2}-3n=0$$

2n ni olish uchun 5n va -3n ni birlashtirish.

$$2n-3n^{2}=0$$

n omili.

$$n\left(2-3n\right)=0$$

Tenglamani yechish uchun n=0 va 2-3n=0 ni yeching.

$$n=0 n=\frac{2}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5\left(n+1\right) ga, n+1,5 ning eng kichik karralisiga ko‘paytiring.

$$5n=\frac{3}{5}n\times 5\left(n+1\right)$$

3 hosil qilish uchun \frac{3}{5} va 5 ni ko'paytirish.

$$5n=3n\left(n+1\right)$$

3n ga n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5n=3n^{2}+3n$$

Ikkala tarafdan 3n^{2} ni ayirish.

$$5n-3n^{2}=3n$$

Ikkala tarafdan 3n ni ayirish.

$$5n-3n^{2}-3n=0$$

2n ni olish uchun 5n va -3n ni birlashtirish.

$$2n-3n^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-3n^{2}+2n=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 2 ni b va 0 ni c bilan almashtiring.

$$n=\frac{-2±\sqrt{2^{2}}}{2\left(-3\right)}$$

2^{2} ning kvadrat ildizini chiqarish.

$$n=\frac{-2±2}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$n=\frac{-2±2}{-6}$$

n=\frac{-2±2}{-6} tenglamasini yeching, bunda ± musbat. -2 ni 2 ga qo'shish.

$$n=\frac{0}{-6}$$

0 ni -6 ga bo'lish.

$$n=0$$

n=\frac{-2±2}{-6} tenglamasini yeching, bunda ± manfiy. -2 dan 2 ni ayirish.

$$n=-\frac{4}{-6}$$

\frac{-4}{-6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n=\frac{2}{3}$$

Tenglama yechildi.

$$n=0 n=\frac{2}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5\left(n+1\right) ga, n+1,5 ning eng kichik karralisiga ko‘paytiring.

$$5n=\frac{3}{5}n\times 5\left(n+1\right)$$

3 hosil qilish uchun \frac{3}{5} va 5 ni ko'paytirish.

$$5n=3n\left(n+1\right)$$

3n ga n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5n=3n^{2}+3n$$

Ikkala tarafdan 3n^{2} ni ayirish.

$$5n-3n^{2}=3n$$

Ikkala tarafdan 3n ni ayirish.

$$5n-3n^{2}-3n=0$$

2n ni olish uchun 5n va -3n ni birlashtirish.

$$2n-3n^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-3n^{2}+2n=0$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3n^{2}+2n}{-3}=\frac{0}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$n^{2}+\frac{2}{-3}n=\frac{0}{-3}$$

2 ni -3 ga bo'lish.

$$n^{2}-\frac{2}{3}n=\frac{0}{-3}$$

0 ni -3 ga bo'lish.

$$n^{2}-\frac{2}{3}n=0$$

-\frac{2}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{3} olish uchun. Keyin, -\frac{1}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-\frac{2}{3}n+\left(-\frac{1}{3}\right)^{2}=\left(-\frac{1}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{3} kvadratini chiqarish.

$$n^{2}-\frac{2}{3}n+\frac{1}{9}=\frac{1}{9}$$

n^{2}-\frac{2}{3}n+\frac{1}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-\frac{1}{3}\right)^{2}=\frac{1}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{1}{3}\right)^{2}}=\sqrt{\frac{1}{9}}$$

Qisqartirish.

$$n-\frac{1}{3}=\frac{1}{3} n-\frac{1}{3}=-\frac{1}{3}$$

\frac{1}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{2}{3} n=0$$