x^2+2/3-x^2+1/4=x+5/12 eching

$$\frac { x ^ { 2 } + 2 } { 3 } - \frac { x ^ { 2 } + 1 } { 4 } = \frac { x + 5 } { 12 }$$

x uchun yechish

$$x=1$$

$$x=0$$

Faktorlash qadamlari

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

$$4\left(x^{2}+2\right)-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3x^{2}-3=x+5$$

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

$$x^{2}+8-3=x+5$$

5 olish uchun 8 dan 3 ni ayirish.

$$x^{2}+5=x+5$$

Ikkala tarafdan x ni ayirish.

$$x^{2}+5-x=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}+5-x-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

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

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, 3,4,12 ning eng kichik karralisiga ko‘paytiring.

$$4\left(x^{2}+2\right)-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3x^{2}-3=x+5$$

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

$$x^{2}+8-3=x+5$$

5 olish uchun 8 dan 3 ni ayirish.

$$x^{2}+5=x+5$$

Ikkala tarafdan x ni ayirish.

$$x^{2}+5-x=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}+5-x-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

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

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.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2}$$

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

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

2 ni 2 ga bo'lish.

$$x=1$$

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

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=1 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$4\left(x^{2}+2\right)-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3\left(x^{2}+1\right)=x+5$$

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

$$4x^{2}+8-3x^{2}-3=x+5$$

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

$$x^{2}+8-3=x+5$$

5 olish uchun 8 dan 3 ni ayirish.

$$x^{2}+5=x+5$$

Ikkala tarafdan x ni ayirish.

$$x^{2}+5-x=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}+5-x-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

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

-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.

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

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

$$x=1 x=0$$