x/2(x^3-1)+(5x^2-1/4)(x-3)+3x^2=x^2(1/2x-1/4)(x+3) eching

$$\frac { x } { 2 } ( x ^ { 3 } - 1 ) + ( \frac { 5 x ^ { 2 } - 1 } { 4 } ) ( x - 3 ) + 3 x ^ { 2 } = x ^ { 2 } ( \frac { 1 } { 2 } x - \frac { 1 } { 4 } ) ( x + 3 )$$

x uchun yechish

$$x=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga, 2,4 ning eng kichik karralisiga ko‘paytiring.

$$2x\left(x^{3}-1\right)+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

2x ga x^{3}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{4}-2x+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

5x^{2}-1 ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{4}-2x+5x^{3}-15x^{2}-x+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

-3x ni olish uchun -2x va -x ni birlashtirish.

$$2x^{4}-3x+5x^{3}-15x^{2}+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

-3x^{2} ni olish uchun -15x^{2} va 12x^{2} ni birlashtirish.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

4x^{2} ga \frac{1}{2}x-\frac{1}{4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=\left(2x^{3}-x^{2}\right)\left(x+3\right)$$

2x^{3}-x^{2} ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=2x^{4}+5x^{3}-3x^{2}$$

Ikkala tarafdan 2x^{4} ni ayirish.

$$2x^{4}-3x+5x^{3}-3x^{2}+3-2x^{4}=5x^{3}-3x^{2}$$

0 ni olish uchun 2x^{4} va -2x^{4} ni birlashtirish.

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

Ikkala tarafdan 5x^{3} ni ayirish.

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

0 ni olish uchun 5x^{3} va -5x^{3} ni birlashtirish.

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

3x^{2} ni ikki tarafga qo’shing.

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

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

$$-3x+3=0$$

Ikkala tarafdan 3 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-3x=-3$$

Ikki tarafini -3 ga bo‘ling.

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

1 ni olish uchun -3 ni -3 ga bo‘ling.

$$x=1$$