x:x^2+(3-2a)x-6a=0 eching

$$x : x ^ { 2 } + ( 3 - 2 a ) x - 6 a = 0$$

a uchun yechish

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

$$x\neq -3\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$x+\left(3-2a\right)xx^{2}-6ax^{2}=0$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$x+\left(3-2a\right)x^{3}-6ax^{2}=0$$

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

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

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

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

Ikkala tarafdan 3x^{3} ni ayirish.

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

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-2x^{3}-6x^{2}\right)a=-x-3x^{3}$$

Tenglama standart shaklda.

$$\left(-2x^{3}-6x^{2}\right)a=-3x^{3}-x$$

Ikki tarafini -2x^{3}-6x^{2} ga bo‘ling.

$$\frac{\left(-2x^{3}-6x^{2}\right)a}{-2x^{3}-6x^{2}}=-\frac{x\left(3x^{2}+1\right)}{-2x^{3}-6x^{2}}$$

-2x^{3}-6x^{2} ga bo'lish -2x^{3}-6x^{2} ga ko'paytirishni bekor qiladi.

$$a=-\frac{x\left(3x^{2}+1\right)}{-2x^{3}-6x^{2}}$$

-x\left(1+3x^{2}\right) ni -2x^{3}-6x^{2} ga bo'lish.

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

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{; }x=\frac{-\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{, }&a\neq \frac{3}{2}\\x=\frac{1}{9}\text{, }&a=\frac{3}{2}\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{; }x=\frac{-\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{, }&a\leq \frac{-2\sqrt{7}-1}{9}\text{ or }\left(a\neq \frac{3}{2}\text{ and }a\geq \frac{2\sqrt{7}-1}{9}\right)\\x=\frac{1}{9}\text{, }&a=\frac{3}{2}\end{matrix}\right,$$