x^3+ax^2+bx+c=0 eching

$$x ^ { 3 } + a x ^ { 2 } + b x + c = 0$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{x^{3}+bx+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$ax^{2}+bx+c=-x^{3}$$

Ikkala tarafdan bx ni ayirish.

$$ax^{2}+c=-x^{3}-bx$$

Ikkala tarafdan c ni ayirish.

$$ax^{2}=-x^{3}-bx-c$$

Tenglama standart shaklda.

$$x^{2}a=-x^{3}-bx-c$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}a}{x^{2}}=\frac{-x^{3}-bx-c}{x^{2}}$$

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

$$a=\frac{-x^{3}-bx-c}{x^{2}}$$

-x^{3}-bx-c ni x^{2} ga bo'lish.

$$a=-\frac{bx+c}{x^{2}}-x$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{x^{3}+ax^{2}+c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$ax^{2}+bx+c=-x^{3}$$

Ikkala tarafdan ax^{2} ni ayirish.

$$bx+c=-x^{3}-ax^{2}$$

Ikkala tarafdan c ni ayirish.

$$bx=-x^{3}-ax^{2}-c$$

Tenglama standart shaklda.

$$xb=-x^{3}-ax^{2}-c$$

Ikki tarafini x ga bo‘ling.

$$\frac{xb}{x}=\frac{-x^{3}-ax^{2}-c}{x}$$

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

$$b=\frac{-x^{3}-ax^{2}-c}{x}$$

-x^{3}-ax^{2}-c ni x ga bo'lish.

$$b=-ax-x^{2}-\frac{c}{x}$$