y=x^2+ax+a eching

$$y = x ^ { 2 } + a x + a$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&y=1\text{ and }x=-1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+ax+a=y$$

Ikkala tarafdan x^{2} ni ayirish.

$$ax+a=y-x^{2}$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x+1 ga bo‘ling.

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

x+1 ga bo'lish x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{y-x^{2}}{x+1}$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&y=1\text{ and }x=-1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+ax+a=y$$

Ikkala tarafdan x^{2} ni ayirish.

$$ax+a=y-x^{2}$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x+1 ga bo‘ling.

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

x+1 ga bo'lish x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{y-x^{2}}{x+1}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{4y+a^{2}-4a}-a}{2}$$

$$x=\frac{-\sqrt{4y+a^{2}-4a}-a}{2}$$

x uchun yechish

$$x=\frac{\sqrt{4y+a^{2}-4a}-a}{2}$$

$$x=\frac{-\sqrt{4y+a^{2}-4a}-a}{2}\text{, }y\geq -\frac{a^{2}}{4}+a$$