2*(x-1)*(2+x)-3/2-(x+2)^2=x*(3-sqrt[5]{-1})-3-x/3 eching

$$\frac { 2 \cdot ( x - 1 ) \cdot ( 2 + x ) - 3 } { 2 } - ( x + 2 ) ^ { 2 } = x \cdot ( 3 - \sqrt[ 5 ] { - 1 } ) - \frac { 3 - x } { 3 }$$

x uchun yechish

$$x=-\frac{39}{44}\approx -0,886363636$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 6 ga, 2,3 ning eng kichik karralisiga ko‘paytiring.

$$3\left(2\left(x-1\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$3\left(\left(2x-2\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$3\left(2x+2x^{2}-4-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

-7 olish uchun -4 dan 3 ni ayirish.

$$3\left(2x+2x^{2}-7\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

3 ga 2x+2x^{2}-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x+6x^{2}-21-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+2\right)^{2} kengaytirilishi uchun ishlating.

$$6x+6x^{2}-21-6\left(x^{2}+4x+4\right)=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

-6 ga x^{2}+4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x+6x^{2}-21-6x^{2}-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

0 ni olish uchun 6x^{2} va -6x^{2} ni birlashtirish.

$$6x-21-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

-18x ni olish uchun 6x va -24x ni birlashtirish.

$$-18x-21-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

-45 olish uchun -21 dan 24 ni ayirish.

$$-18x-45=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

\sqrt[5]{-1} ni hisoblab, -1 natijasiga ega bo‘ling.

$$-18x-45=6x\left(3-\left(-1\right)\right)-2\left(3-x\right)$$

-1 ning teskarisi 1 ga teng.

$$-18x-45=6x\left(3+1\right)-2\left(3-x\right)$$

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

$$-18x-45=6x\times 4-2\left(3-x\right)$$

24 hosil qilish uchun 6 va 4 ni ko'paytirish.

$$-18x-45=24x-2\left(3-x\right)$$

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

$$-18x-45=24x-6+2x$$

26x ni olish uchun 24x va 2x ni birlashtirish.

$$-18x-45=26x-6$$

Ikkala tarafdan 26x ni ayirish.

$$-18x-45-26x=-6$$

-44x ni olish uchun -18x va -26x ni birlashtirish.

$$-44x-45=-6$$

45 ni ikki tarafga qo’shing.

$$-44x=-6+45$$

39 olish uchun -6 va 45'ni qo'shing.

$$-44x=39$$

Ikki tarafini -44 ga bo‘ling.

$$x=\frac{39}{-44}$$

\frac{39}{-44} kasri manfiy belgini olib tashlash bilan -\frac{39}{44} sifatida qayta yozilishi mumkin.

$$x=-\frac{39}{44}$$