x-1/2x-3=2/x eching

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

x uchun yechish

$$x=2$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,\frac{3}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(2x-3\right) ga, 2x-3,x ning eng kichik karralisiga ko‘paytiring.

$$x\left(x-1\right)=\left(2x-3\right)\times 2$$

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

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

2x-3 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-x=4x-6$$

Ikkala tarafdan 4x ni ayirish.

$$x^{2}-x-4x=-6$$

-5x ni olish uchun -x va -4x ni birlashtirish.

$$x^{2}-5x=-6$$

6 ni ikki tarafga qo’shing.

$$x^{2}-5x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -5 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 6}}{2}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-24}}{2}$$

25 ni -24 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±1}{2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±1}{2}$$

x=\frac{5±1}{2} tenglamasini yeching, bunda ± musbat. 5 ni 1 ga qo'shish.

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

6 ni 2 ga bo'lish.

$$x=3$$

x=\frac{5±1}{2} tenglamasini yeching, bunda ± manfiy. 5 dan 1 ni ayirish.

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

4 ni 2 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=3 x=2$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0,\frac{3}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(2x-3\right) ga, 2x-3,x ning eng kichik karralisiga ko‘paytiring.

$$x\left(x-1\right)=\left(2x-3\right)\times 2$$

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

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

2x-3 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-x=4x-6$$

Ikkala tarafdan 4x ni ayirish.

$$x^{2}-x-4x=-6$$

-5x ni olish uchun -x va -4x ni birlashtirish.

$$x^{2}-5x=-6$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=-6+\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=-6+\frac{25}{4}$$

-6 ni \frac{25}{4} ga qo'shish.

$$x^{2}-5x+\frac{25}{4}=\frac{1}{4}$$

x^{2}-5x+\frac{25}{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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-\frac{5}{2}=\frac{1}{2} x-\frac{5}{2}=-\frac{1}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=3 x=2$$