4v^2-12v=0 eching

$$4 v ^ { 2 } - 12 v = 0$$

v uchun yechish

$$v=3$$

$$v=0$$

Faktorlash qadamlari

v omili.

$$v\left(4v-12\right)=0$$

Tenglamani yechish uchun v=0 va 4v-12=0 ni yeching.

$$v=0 v=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$4v^{2}-12v=0$$

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

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

\left(-12\right)^{2} ning kvadrat ildizini chiqarish.

$$v=\frac{-\left(-12\right)±12}{2\times 4}$$

-12 ning teskarisi 12 ga teng.

$$v=\frac{12±12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$v=\frac{12±12}{8}$$

v=\frac{12±12}{8} tenglamasini yeching, bunda ± musbat. 12 ni 12 ga qo'shish.

$$v=\frac{24}{8}$$

24 ni 8 ga bo'lish.

$$v=3$$

v=\frac{12±12}{8} tenglamasini yeching, bunda ± manfiy. 12 dan 12 ni ayirish.

$$v=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$v=0$$

Tenglama yechildi.

$$v=3 v=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$4v^{2}-12v=0$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4v^{2}-12v}{4}=\frac{0}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$v^{2}+\left(-\frac{12}{4}\right)v=\frac{0}{4}$$

-12 ni 4 ga bo'lish.

$$v^{2}-3v=\frac{0}{4}$$

0 ni 4 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

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

v^{2}-3v+\frac{9}{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.

$$\left(v-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(v-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$v-\frac{3}{2}=\frac{3}{2} v-\frac{3}{2}=-\frac{3}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$v=3 v=0$$