x^2=4x+1/y eching

$$x ^ { 2 } = \frac { 4 x + 1 } { y }$$

y uchun yechish

$$y=\frac{4x+1}{x^{2}}$$

$$x\neq -\frac{1}{4}\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$yx^{2}=4x+1$$

Tenglama standart shaklda.

$$x^{2}y=4x+1$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}y}{x^{2}}=\frac{4x+1}{x^{2}}$$

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

$$y=\frac{4x+1}{x^{2}}$$

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{4x+1}{x^{2}}\text{, }y\neq 0$$

x uchun yechish (complex solution)

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

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0$$

x uchun yechish

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

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0\text{ and }y\geq -4$$