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.

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

q ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

$$\left(-x\right)p=q-x^{3}$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)p}{-x}=\frac{q-x^{3}}{-x}$$

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

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

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

$$p=x^{2}-\frac{q}{x}$$

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.

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

q ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

$$\left(-x\right)p=q-x^{3}$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)p}{-x}=\frac{q-x^{3}}{-x}$$

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

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

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

$$p=x^{2}-\frac{q}{x}$$

q uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

px ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-q}{-1}=\frac{x\left(p-x^{2}\right)}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$q=\frac{x\left(p-x^{2}\right)}{-1}$$

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

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