(6v-9)(2v+1)=7v^2-38-33 eching

$$( 6 v - 9 ) ( 2 v + 1 ) = 7 v ^ { 2 } - 38 - 33$$

v uchun yechish

$$v=\frac{6+\sqrt{274}i}{5}\approx 1,2+3,310589071i$$

$$v=\frac{-\sqrt{274}i+6}{5}\approx 1,2-3,310589071i$$

Kvadrat tenglamalaridan foydalanish qoidalari

6v-9 ga 2v+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12v^{2}-12v-9=7v^{2}-38-33$$

-71 olish uchun -38 dan 33 ni ayirish.

$$12v^{2}-12v-9=7v^{2}-71$$

Ikkala tarafdan 7v^{2} ni ayirish.

$$12v^{2}-12v-9-7v^{2}=-71$$

5v^{2} ni olish uchun 12v^{2} va -7v^{2} ni birlashtirish.

$$5v^{2}-12v-9=-71$$

71 ni ikki tarafga qo’shing.

$$5v^{2}-12v-9+71=0$$

62 olish uchun -9 va 71'ni qo'shing.

$$5v^{2}-12v+62=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -12 ni b va 62 ni c bilan almashtiring.

$$v=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 5\times 62}}{2\times 5}$$

-12 kvadratini chiqarish.

$$v=\frac{-\left(-12\right)±\sqrt{144-4\times 5\times 62}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$v=\frac{-\left(-12\right)±\sqrt{144-20\times 62}}{2\times 5}$$

-20 ni 62 marotabaga ko'paytirish.

$$v=\frac{-\left(-12\right)±\sqrt{144-1240}}{2\times 5}$$

144 ni -1240 ga qo'shish.

$$v=\frac{-\left(-12\right)±\sqrt{-1096}}{2\times 5}$$

-1096 ning kvadrat ildizini chiqarish.

$$v=\frac{-\left(-12\right)±2\sqrt{274}i}{2\times 5}$$

-12 ning teskarisi 12 ga teng.

$$v=\frac{12±2\sqrt{274}i}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$v=\frac{12±2\sqrt{274}i}{10}$$

v=\frac{12±2\sqrt{274}i}{10} tenglamasini yeching, bunda ± musbat. 12 ni 2i\sqrt{274} ga qo'shish.

$$v=\frac{12+2\sqrt{274}i}{10}$$

12+2i\sqrt{274} ni 10 ga bo'lish.

$$v=\frac{6+\sqrt{274}i}{5}$$

v=\frac{12±2\sqrt{274}i}{10} tenglamasini yeching, bunda ± manfiy. 12 dan 2i\sqrt{274} ni ayirish.

$$v=\frac{-2\sqrt{274}i+12}{10}$$

12-2i\sqrt{274} ni 10 ga bo'lish.

$$v=\frac{-\sqrt{274}i+6}{5}$$

Tenglama yechildi.

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

6v-9 ga 2v+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12v^{2}-12v-9=7v^{2}-38-33$$

-71 olish uchun -38 dan 33 ni ayirish.

$$12v^{2}-12v-9=7v^{2}-71$$

Ikkala tarafdan 7v^{2} ni ayirish.

$$12v^{2}-12v-9-7v^{2}=-71$$

5v^{2} ni olish uchun 12v^{2} va -7v^{2} ni birlashtirish.

$$5v^{2}-12v-9=-71$$

9 ni ikki tarafga qo’shing.

$$5v^{2}-12v=-71+9$$

-62 olish uchun -71 va 9'ni qo'shing.

$$5v^{2}-12v=-62$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5v^{2}-12v}{5}=-\frac{62}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$v^{2}-\frac{12}{5}v=-\frac{62}{5}$$

-\frac{12}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{6}{5} olish uchun. Keyin, -\frac{6}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$v^{2}-\frac{12}{5}v+\left(-\frac{6}{5}\right)^{2}=-\frac{62}{5}+\left(-\frac{6}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{6}{5} kvadratini chiqarish.

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{62}{5}+\frac{36}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{62}{5} ni \frac{36}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{274}{25}$$

v^{2}-\frac{12}{5}v+\frac{36}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(v-\frac{6}{5}\right)^{2}=-\frac{274}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(v-\frac{6}{5}\right)^{2}}=\sqrt{-\frac{274}{25}}$$

Qisqartirish.

$$v-\frac{6}{5}=\frac{\sqrt{274}i}{5} v-\frac{6}{5}=-\frac{\sqrt{274}i}{5}$$

\frac{6}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$