n/n-4+n=12-4n/n-4 eching

$$\frac { n } { n - 4 } + n = \frac { 12 - 4 n } { n - 4 }$$

n uchun yechish

$$n=-4$$

$$n=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n-4 ga ko'paytirish.

$$n+\left(n-4\right)n=12-4n$$

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

$$n+n^{2}-4n=12-4n$$

-3n ni olish uchun n va -4n ni birlashtirish.

$$-3n+n^{2}=12-4n$$

Ikkala tarafdan 12 ni ayirish.

$$-3n+n^{2}-12=-4n$$

4n ni ikki tarafga qo’shing.

$$-3n+n^{2}-12+4n=0$$

n ni olish uchun -3n va 4n ni birlashtirish.

$$n+n^{2}-12=0$$

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.

$$n^{2}+n-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1 ni b va -12 ni c bilan almashtiring.

$$n=\frac{-1±\sqrt{1^{2}-4\left(-12\right)}}{2}$$

1 kvadratini chiqarish.

$$n=\frac{-1±\sqrt{1-4\left(-12\right)}}{2}$$

-4 ni -12 marotabaga ko'paytirish.

$$n=\frac{-1±\sqrt{1+48}}{2}$$

1 ni 48 ga qo'shish.

$$n=\frac{-1±\sqrt{49}}{2}$$

49 ning kvadrat ildizini chiqarish.

$$n=\frac{-1±7}{2}$$

n=\frac{-1±7}{2} tenglamasini yeching, bunda ± musbat. -1 ni 7 ga qo'shish.

$$n=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$n=3$$

n=\frac{-1±7}{2} tenglamasini yeching, bunda ± manfiy. -1 dan 7 ni ayirish.

$$n=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$n=-4$$

Tenglama yechildi.

$$n=3 n=-4$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n-4 ga ko'paytirish.

$$n+\left(n-4\right)n=12-4n$$

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

$$n+n^{2}-4n=12-4n$$

-3n ni olish uchun n va -4n ni birlashtirish.

$$-3n+n^{2}=12-4n$$

4n ni ikki tarafga qo’shing.

$$-3n+n^{2}+4n=12$$

n ni olish uchun -3n va 4n ni birlashtirish.

$$n+n^{2}=12$$

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

$$n^{2}+n=12$$

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

$$n^{2}+n+\left(\frac{1}{2}\right)^{2}=12+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$n^{2}+n+\frac{1}{4}=12+\frac{1}{4}$$

12 ni \frac{1}{4} ga qo'shish.

$$n^{2}+n+\frac{1}{4}=\frac{49}{4}$$

n^{2}+n+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n+\frac{1}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+\frac{1}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$n+\frac{1}{2}=\frac{7}{2} n+\frac{1}{2}=-\frac{7}{2}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$n=3 n=-4$$