a^2+bx^2+c=0 eching

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

b uchun yechish (complex solution)

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan a^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$bx^{2}+c=-a^{2}$$

Ikkala tarafdan c ni ayirish.

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

Tenglama standart shaklda.

$$x^{2}b=-a^{2}-c$$

Ikki tarafini x^{2} ga bo‘ling.

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

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

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

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

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

b uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan a^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$bx^{2}+c=-a^{2}$$

Ikkala tarafdan c ni ayirish.

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

Tenglama standart shaklda.

$$x^{2}b=-a^{2}-c$$

Ikki tarafini x^{2} ga bo‘ling.

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

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

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

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

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

a uchun yechish (complex solution)

$$a=-i\sqrt{bx^{2}+c}$$

$$a=i\sqrt{bx^{2}+c}$$

a uchun yechish

$$a=\sqrt{-bx^{2}-c}$$

$$a=-\sqrt{-bx^{2}-c}\text{, }b\leq -\frac{c}{x^{2}}\text{ or }x=0$$