x+1/x-3=9 eching

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

x uchun yechish

$$x=2\sqrt{2}+6\approx 8,828427125$$

$$x=6-2\sqrt{2}\approx 3,171572875$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-3 ga ko'paytirish.

$$\left(x-3\right)x+1=9\left(x-3\right)$$

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

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

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

$$x^{2}-3x+1=9x-27$$

Ikkala tarafdan 9x ni ayirish.

$$x^{2}-3x+1-9x=-27$$

-12x ni olish uchun -3x va -9x ni birlashtirish.

$$x^{2}-12x+1=-27$$

27 ni ikki tarafga qo’shing.

$$x^{2}-12x+1+27=0$$

28 olish uchun 1 va 27'ni qo'shing.

$$x^{2}-12x+28=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va 28 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 28}}{2}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 28}}{2}$$

-4 ni 28 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-112}}{2}$$

144 ni -112 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{32}}{2}$$

32 ning kvadrat ildizini chiqarish.

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

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±4\sqrt{2}}{2}$$

x=\frac{12±4\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 12 ni 4\sqrt{2} ga qo'shish.

$$x=\frac{4\sqrt{2}+12}{2}$$

12+4\sqrt{2} ni 2 ga bo'lish.

$$x=2\sqrt{2}+6$$

x=\frac{12±4\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 4\sqrt{2} ni ayirish.

$$x=\frac{12-4\sqrt{2}}{2}$$

12-4\sqrt{2} ni 2 ga bo'lish.

$$x=6-2\sqrt{2}$$

Tenglama yechildi.

$$x=2\sqrt{2}+6 x=6-2\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-3 ga ko'paytirish.

$$\left(x-3\right)x+1=9\left(x-3\right)$$

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

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

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

$$x^{2}-3x+1=9x-27$$

Ikkala tarafdan 9x ni ayirish.

$$x^{2}-3x+1-9x=-27$$

-12x ni olish uchun -3x va -9x ni birlashtirish.

$$x^{2}-12x+1=-27$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}-12x=-27-1$$

-28 olish uchun -27 dan 1 ni ayirish.

$$x^{2}-12x=-28$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=-28+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=-28+36$$

-28 ni 36 ga qo'shish.

$$x^{2}-12x+36=8$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=8$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{8}$$

Qisqartirish.

$$x-6=2\sqrt{2} x-6=-2\sqrt{2}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{2}+6 x=6-2\sqrt{2}$$