32n/24n=4n^2/3n eching

$$\frac { 32 n } { 24 n } = \frac { 4 n ^ { 2 } } { 3 n }$$

n uchun yechish

$$n=1$$

Faktorlash qadamlari

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 24n ga, 24n,3n ning eng kichik karralisiga ko‘paytiring.

$$32n=8\times 4n^{2}$$

32 hosil qilish uchun 8 va 4 ni ko'paytirish.

$$32n=32n^{2}$$

Ikkala tarafdan 32n^{2} ni ayirish.

$$32n-32n^{2}=0$$

n omili.

$$n\left(32-32n\right)=0$$

Tenglamani yechish uchun n=0 va 32-32n=0 ni yeching.

$$n=0 n=1$$

n qiymati 0 teng bo‘lmaydi.

$$n=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 24n ga, 24n,3n ning eng kichik karralisiga ko‘paytiring.

$$32n=8\times 4n^{2}$$

32 hosil qilish uchun 8 va 4 ni ko'paytirish.

$$32n=32n^{2}$$

Ikkala tarafdan 32n^{2} ni ayirish.

$$32n-32n^{2}=0$$

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.

$$-32n^{2}+32n=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -32 ni a, 32 ni b va 0 ni c bilan almashtiring.

$$n=\frac{-32±\sqrt{32^{2}}}{2\left(-32\right)}$$

32^{2} ning kvadrat ildizini chiqarish.

$$n=\frac{-32±32}{2\left(-32\right)}$$

2 ni -32 marotabaga ko'paytirish.

$$n=\frac{-32±32}{-64}$$

n=\frac{-32±32}{-64} tenglamasini yeching, bunda ± musbat. -32 ni 32 ga qo'shish.

$$n=\frac{0}{-64}$$

0 ni -64 ga bo'lish.

$$n=0$$

n=\frac{-32±32}{-64} tenglamasini yeching, bunda ± manfiy. -32 dan 32 ni ayirish.

$$n=-\frac{64}{-64}$$

-64 ni -64 ga bo'lish.

$$n=1$$

Tenglama yechildi.

$$n=0 n=1$$

n qiymati 0 teng bo‘lmaydi.

$$n=1$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 24n ga, 24n,3n ning eng kichik karralisiga ko‘paytiring.

$$32n=8\times 4n^{2}$$

32 hosil qilish uchun 8 va 4 ni ko'paytirish.

$$32n=32n^{2}$$

Ikkala tarafdan 32n^{2} ni ayirish.

$$32n-32n^{2}=0$$

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

$$-32n^{2}+32n=0$$

Ikki tarafini -32 ga bo‘ling.

$$\frac{-32n^{2}+32n}{-32}=\frac{0}{-32}$$

-32 ga bo'lish -32 ga ko'paytirishni bekor qiladi.

$$n^{2}+\frac{32}{-32}n=\frac{0}{-32}$$

32 ni -32 ga bo'lish.

$$n^{2}-n=\frac{0}{-32}$$

0 ni -32 ga bo'lish.

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

-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.

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

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

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$n=1 n=0$$

n qiymati 0 teng bo‘lmaydi.

$$n=1$$