3x(x-1)=x-1 eching

$$3x(x-1)=x-1$$

x uchun yechish

$$x=\frac{1}{3}\approx 0,333333333$$

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-3x=x-1$$

Ikkala tarafdan x ni ayirish.

$$3x^{2}-3x-x=-1$$

-4x ni olish uchun -3x va -x ni birlashtirish.

$$3x^{2}-4x=-1$$

1 ni ikki tarafga qo’shing.

$$3x^{2}-4x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -4 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 3}}{2\times 3}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 3}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-12}}{2\times 3}$$

16 ni -12 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{4}}{2\times 3}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2}{2\times 3}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{4±2}{6}$$

x=\frac{4±2}{6} tenglamasini yeching, bunda ± musbat. 4 ni 2 ga qo'shish.

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

6 ni 6 ga bo'lish.

$$x=1$$

x=\frac{4±2}{6} tenglamasini yeching, bunda ± manfiy. 4 dan 2 ni ayirish.

$$x=\frac{2}{6}$$

\frac{2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{3}$$

Tenglama yechildi.

$$x=1 x=\frac{1}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-3x=x-1$$

Ikkala tarafdan x ni ayirish.

$$3x^{2}-3x-x=-1$$

-4x ni olish uchun -3x va -x ni birlashtirish.

$$3x^{2}-4x=-1$$

Ikki tarafini 3 ga bo‘ling.

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

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

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

-\frac{4}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{2}{3} olish uchun. Keyin, -\frac{2}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

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

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=-\frac{1}{3}+\frac{4}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{3} ni \frac{4}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{1}{9}$$

x^{2}-\frac{4}{3}x+\frac{4}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{2}{3}\right)^{2}=\frac{1}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{1}{9}}$$

Qisqartirish.

$$x-\frac{2}{3}=\frac{1}{3} x-\frac{2}{3}=-\frac{1}{3}$$

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

$$x=1 x=\frac{1}{3}$$