(2x-1)(2x+1)/3=3x-2/6+x^2/3 eching

$$\frac { ( 2 x - 1 ) ( 2 x + 1 ) } { 3 } = \frac { 3 x - 2 } { 6 } + \frac { x ^ { 2 } } { 3 }$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 6 ga, 3,6 ning eng kichik karralisiga ko‘paytiring.

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

2 ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(4x-2\right)\left(2x+1\right)=3x-2+2x^{2}$$

4x-2 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8x^{2}-2=3x-2+2x^{2}$$

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-2-3x=-2+2x^{2}$$

Ikkala tarafdan -2 ni ayirish.

$$8x^{2}-2-3x-\left(-2\right)=2x^{2}$$

-2 ning teskarisi 2 ga teng.

$$8x^{2}-2-3x+2=2x^{2}$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$8x^{2}-2-3x+2-2x^{2}=0$$

0 olish uchun -2 va 2'ni qo'shing.

$$8x^{2}-3x-2x^{2}=0$$

6x^{2} ni olish uchun 8x^{2} va -2x^{2} ni birlashtirish.

$$6x^{2}-3x=0$$

x omili.

$$x\left(6x-3\right)=0$$

Tenglamani yechish uchun x=0 va 6x-3=0 ni yeching.

$$x=0 x=\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 6 ga, 3,6 ning eng kichik karralisiga ko‘paytiring.

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

2 ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(4x-2\right)\left(2x+1\right)=3x-2+2x^{2}$$

4x-2 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8x^{2}-2=3x-2+2x^{2}$$

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-2-3x=-2+2x^{2}$$

Ikkala tarafdan -2 ni ayirish.

$$8x^{2}-2-3x-\left(-2\right)=2x^{2}$$

-2 ning teskarisi 2 ga teng.

$$8x^{2}-2-3x+2=2x^{2}$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$8x^{2}-2-3x+2-2x^{2}=0$$

0 olish uchun -2 va 2'ni qo'shing.

$$8x^{2}-3x-2x^{2}=0$$

6x^{2} ni olish uchun 8x^{2} va -2x^{2} ni birlashtirish.

$$6x^{2}-3x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -3 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 6}$$

\left(-3\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±3}{2\times 6}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{3±3}{12}$$

x=\frac{3±3}{12} tenglamasini yeching, bunda ± musbat. 3 ni 3 ga qo'shish.

$$x=\frac{6}{12}$$

\frac{6}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

x=\frac{3±3}{12} tenglamasini yeching, bunda ± manfiy. 3 dan 3 ni ayirish.

$$x=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{2} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 6 ga, 3,6 ning eng kichik karralisiga ko‘paytiring.

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

2 ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(4x-2\right)\left(2x+1\right)=3x-2+2x^{2}$$

4x-2 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8x^{2}-2=3x-2+2x^{2}$$

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-2-3x=-2+2x^{2}$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$8x^{2}-2-3x-2x^{2}=-2$$

6x^{2} ni olish uchun 8x^{2} va -2x^{2} ni birlashtirish.

$$6x^{2}-2-3x=-2$$

2 ni ikki tarafga qo’shing.

$$6x^{2}-3x=-2+2$$

0 olish uchun -2 va 2'ni qo'shing.

$$6x^{2}-3x=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-3x}{6}=\frac{0}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{3}{6}\right)x=\frac{0}{6}$$

\frac{-3}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{2}x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}-\frac{1}{2}x=0$$

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{16}$$

x^{2}-\frac{1}{2}x+\frac{1}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{1}{4} x-\frac{1}{4}=-\frac{1}{4}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{2} x=0$$