x-1=3x+1/x-1 eching

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

x uchun yechish

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

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$\left(x-1\right)x+\left(x-1\right)\left(-1\right)=3x\left(x-1\right)+1$$

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

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

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

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

-2x ni olish uchun -x va -x ni birlashtirish.

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

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

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

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

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

3x ni ikki tarafga qo’shing.

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

x ni olish uchun -2x va 3x ni birlashtirish.

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

Ikkala tarafdan 1 ni ayirish.

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

0 olish uchun 1 dan 1 ni ayirish.

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

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

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

1^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-1±1}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1±1}{-4}$$

x=\frac{-1±1}{-4} tenglamasini yeching, bunda ± musbat. -1 ni 1 ga qo'shish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

x=\frac{-1±1}{-4} tenglamasini yeching, bunda ± manfiy. -1 dan 1 ni ayirish.

$$x=-\frac{2}{-4}$$

\frac{-2}{-4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$\left(x-1\right)x+\left(x-1\right)\left(-1\right)=3x\left(x-1\right)+1$$

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

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

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

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

-2x ni olish uchun -x va -x ni birlashtirish.

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

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

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

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

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

3x ni ikki tarafga qo’shing.

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

x ni olish uchun -2x va 3x ni birlashtirish.

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

Ikkala tarafdan 1 ni ayirish.

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

0 olish uchun 1 dan 1 ni ayirish.

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

Ikki tarafini -2 ga bo‘ling.

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

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

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

1 ni -2 ga bo'lish.

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

0 ni -2 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.

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