x^2+2/3+x+7/12=1+x^2+1/4 eching

$$\frac { x ^ { 2 } + 2 } { 3 } + \frac { x + 7 } { 12 } = 1 + \frac { x ^ { 2 } + 1 } { 4 }$$

x uchun yechish

$$x=-1$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 12 ga, 3,12,4 ning eng kichik karralisiga ko‘paytiring.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

4 ga x^{2}+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

15 olish uchun 8 va 7'ni qo'shing.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

3 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+15+x=12+3x^{2}+3$$

15 olish uchun 12 va 3'ni qo'shing.

$$4x^{2}+15+x=15+3x^{2}$$

Ikkala tarafdan 15 ni ayirish.

$$4x^{2}+15+x-15=3x^{2}$$

0 olish uchun 15 dan 15 ni ayirish.

$$4x^{2}+x=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$4x^{2}+x-3x^{2}=0$$

x^{2} ni olish uchun 4x^{2} va -3x^{2} ni birlashtirish.

$$x^{2}+x=0$$

x omili.

$$x\left(x+1\right)=0$$

Tenglamani yechish uchun x=0 va x+1=0 ni yeching.

$$x=0 x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 12 ga, 3,12,4 ning eng kichik karralisiga ko‘paytiring.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

4 ga x^{2}+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

15 olish uchun 8 va 7'ni qo'shing.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

3 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+15+x=12+3x^{2}+3$$

15 olish uchun 12 va 3'ni qo'shing.

$$4x^{2}+15+x=15+3x^{2}$$

Ikkala tarafdan 15 ni ayirish.

$$4x^{2}+15+x-15=3x^{2}$$

0 olish uchun 15 dan 15 ni ayirish.

$$4x^{2}+x=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$4x^{2}+x-3x^{2}=0$$

x^{2} ni olish uchun 4x^{2} va -3x^{2} ni birlashtirish.

$$x^{2}+x=0$$

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 0 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}}}{2}$$

1^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-1±1}{2}$$

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

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

0 ni 2 ga bo'lish.

$$x=0$$

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

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

-2 ni 2 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=0 x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 12 ga, 3,12,4 ning eng kichik karralisiga ko‘paytiring.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

4 ga x^{2}+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

15 olish uchun 8 va 7'ni qo'shing.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

3 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+15+x=12+3x^{2}+3$$

15 olish uchun 12 va 3'ni qo'shing.

$$4x^{2}+15+x=15+3x^{2}$$

Ikkala tarafdan 15 ni ayirish.

$$4x^{2}+15+x-15=3x^{2}$$

0 olish uchun 15 dan 15 ni ayirish.

$$4x^{2}+x=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$4x^{2}+x-3x^{2}=0$$

x^{2} ni olish uchun 4x^{2} va -3x^{2} ni birlashtirish.

$$x^{2}+x=0$$

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.

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

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

$$x^{2}+x+\frac{1}{4}=\frac{1}{4}$$

x^{2}+x+\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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

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

$$x=0 x=-1$$