x^3+px+q=0 eching

$$x ^ { 3 } + p x + q = 0$$

p uchun yechish (complex solution)

$$\left\{\begin{matrix}p=-\frac{x^{3}+q}{x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&q=0\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$px+q=-x^{3}$$

Ikkala tarafdan q ni ayirish.

$$px=-x^{3}-q$$

Tenglama standart shaklda.

$$xp=-x^{3}-q$$

Ikki tarafini x ga bo‘ling.

$$\frac{xp}{x}=\frac{-x^{3}-q}{x}$$

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

$$p=\frac{-x^{3}-q}{x}$$

-x^{3}-q ni x ga bo'lish.

$$p=-\frac{x^{3}+q}{x}$$

p uchun yechish

$$\left\{\begin{matrix}p=-\frac{x^{3}+q}{x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }q=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$px+q=-x^{3}$$

Ikkala tarafdan q ni ayirish.

$$px=-x^{3}-q$$

Tenglama standart shaklda.

$$xp=-x^{3}-q$$

Ikki tarafini x ga bo‘ling.

$$\frac{xp}{x}=\frac{-x^{3}-q}{x}$$

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

$$p=\frac{-x^{3}-q}{x}$$

-x^{3}-q ni x ga bo'lish.

$$p=-\frac{x^{3}+q}{x}$$

q uchun yechish

$$q=-x\left(x^{2}+p\right)$$

Yechim qadamlari

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

$$px+q=-x^{3}$$

Ikkala tarafdan px ni ayirish.

$$q=-x^{3}-px$$