y=x^2+px-4/x+r eching

$$y = \frac { x ^ { 2 } + p x - 4 } { x + r }$$

p uchun yechish

$$\left\{\begin{matrix}p=\frac{4+ry+xy-x^{2}}{x}\text{, }&x\neq 0\text{ and }x\neq -r\\p\in \mathrm{R}\text{, }&y=-\frac{4}{r}\text{ and }x=0\text{ and }r\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x+r ga ko'paytirish.

$$y\left(x+r\right)=x^{2}+px-4$$

y ga x+r ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$yx+yr=x^{2}+px-4$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+px-4=yx+yr$$

Ikkala tarafdan x^{2} ni ayirish.

$$px-4=yx+yr-x^{2}$$

4 ni ikki tarafga qo’shing.

$$px=yx+yr-x^{2}+4$$

Tenglama standart shaklda.

$$xp=4+ry+xy-x^{2}$$

Ikki tarafini x ga bo‘ling.

$$\frac{xp}{x}=\frac{4+ry+xy-x^{2}}{x}$$

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

$$p=\frac{4+ry+xy-x^{2}}{x}$$

yx+yr-x^{2}+4 ni x ga bo'lish.

$$p=\frac{ry+4}{x}+y-x$$

r uchun yechish

$$\left\{\begin{matrix}r=-\frac{4-px+xy-x^{2}}{y}\text{, }&\left(x=0\text{ or }p\neq -x+\frac{4}{x}\right)\text{ and }y\neq 0\text{ and }x\neq \frac{-\sqrt{p^{2}+16}-p}{2}\text{ and }x\neq \frac{\sqrt{p^{2}+16}-p}{2}\\r\neq -x\text{, }&y=0\text{ and }p=-x+\frac{4}{x}\text{ and }x\neq 0\end{matrix}\right,$$