x-1/x+2=10/3x-2 eching

$$\frac { x - 1 } { x + 2 } = \frac { 10 } { 3 x - 2 }$$

x uchun yechish

$$x=-1$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\left(3x-2\right)\left(x-1\right)=\left(x+2\right)\times 10$$

3x-2 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-5x+2=\left(x+2\right)\times 10$$

x+2 ga 10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-5x+2=10x+20$$

Ikkala tarafdan 10x ni ayirish.

$$3x^{2}-5x+2-10x=20$$

-15x ni olish uchun -5x va -10x ni birlashtirish.

$$3x^{2}-15x+2=20$$

Ikkala tarafdan 20 ni ayirish.

$$3x^{2}-15x+2-20=0$$

-18 olish uchun 2 dan 20 ni ayirish.

$$3x^{2}-15x-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -15 ni b va -18 ni c bilan almashtiring.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 3\left(-18\right)}}{2\times 3}$$

-15 kvadratini chiqarish.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 3\left(-18\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225-12\left(-18\right)}}{2\times 3}$$

-12 ni -18 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225+216}}{2\times 3}$$

225 ni 216 ga qo'shish.

$$x=\frac{-\left(-15\right)±\sqrt{441}}{2\times 3}$$

441 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±21}{2\times 3}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±21}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{15±21}{6}$$

x=\frac{15±21}{6} tenglamasini yeching, bunda ± musbat. 15 ni 21 ga qo'shish.

$$x=\frac{36}{6}$$

36 ni 6 ga bo'lish.

$$x=6$$

x=\frac{15±21}{6} tenglamasini yeching, bunda ± manfiy. 15 dan 21 ni ayirish.

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

-6 ni 6 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=6 x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$\left(3x-2\right)\left(x-1\right)=\left(x+2\right)\times 10$$

3x-2 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-5x+2=\left(x+2\right)\times 10$$

x+2 ga 10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-5x+2=10x+20$$

Ikkala tarafdan 10x ni ayirish.

$$3x^{2}-5x+2-10x=20$$

-15x ni olish uchun -5x va -10x ni birlashtirish.

$$3x^{2}-15x+2=20$$

Ikkala tarafdan 2 ni ayirish.

$$3x^{2}-15x=20-2$$

18 olish uchun 20 dan 2 ni ayirish.

$$3x^{2}-15x=18$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-15x}{3}=\frac{18}{3}$$

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

$$x^{2}+\left(-\frac{15}{3}\right)x=\frac{18}{3}$$

-15 ni 3 ga bo'lish.

$$x^{2}-5x=\frac{18}{3}$$

18 ni 3 ga bo'lish.

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

-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.

$$x^{2}-5x+\frac{25}{4}=\frac{49}{4}$$

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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{7}{2} x-\frac{5}{2}=-\frac{7}{2}$$

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

$$x=6 x=-1$$