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

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

x uchun yechish

$$x = \frac{3 \sqrt{2}}{2} \approx 2,121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2,121320344$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -2,-1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right)\left(x+2\right) ga, x^{3}+2x^{2}-x-2,1-x,x+1 ning eng kichik karralisiga ko‘paytiring.

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

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

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

3 olish uchun 1 va 2'ni qo'shing.

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

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

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

x^{2}+x-2 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3+3x+x^{2}=3x^{2}+3x-6$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$3+3x+x^{2}-3x^{2}=3x-6$$

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

$$3+3x-2x^{2}=3x-6$$

Ikkala tarafdan 3x ni ayirish.

$$3+3x-2x^{2}-3x=-6$$

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

$$3-2x^{2}=-6$$

Ikkala tarafdan 3 ni ayirish.

$$-2x^{2}=-6-3$$

-9 olish uchun -6 dan 3 ni ayirish.

$$-2x^{2}=-9$$

Ikki tarafini -2 ga bo‘ling.

$$x^{2}=\frac{-9}{-2}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-9}{-2} kasrini \frac{9}{2} ga soddalashtirish mumkin.

$$x^{2}=\frac{9}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -2,-1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right)\left(x+2\right) ga, x^{3}+2x^{2}-x-2,1-x,x+1 ning eng kichik karralisiga ko‘paytiring.

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

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

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

3 olish uchun 1 va 2'ni qo'shing.

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

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

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

x^{2}+x-2 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3+3x+x^{2}=3x^{2}+3x-6$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$3+3x+x^{2}-3x^{2}=3x-6$$

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

$$3+3x-2x^{2}=3x-6$$

Ikkala tarafdan 3x ni ayirish.

$$3+3x-2x^{2}-3x=-6$$

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

$$3-2x^{2}=-6$$

6 ni ikki tarafga qo’shing.

$$3-2x^{2}+6=0$$

9 olish uchun 3 va 6'ni qo'shing.

$$9-2x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-2x^{2}+9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 0 ni b va 9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 9}}{2\left(-2\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 9}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{8\times 9}}{2\left(-2\right)}$$

8 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{72}}{2\left(-2\right)}$$

72 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{2}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±6\sqrt{2}}{-4}$$

x=\frac{0±6\sqrt{2}}{-4} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±6\sqrt{2}}{-4} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{3\sqrt{2}}{2}$$

Tenglama yechildi.

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