212x+3y/2^2+y^2=9 eching

$$\frac { 212 x + 3 y } { 2 ^ { 2 } + y ^ { 2 } } = 9$$

x uchun yechish (complex solution)

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

$$y\neq -2i\text{ and }y\neq 2i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(y-2i\right)\left(y+2i\right) ga ko'paytirish.

$$212x+3y=9\left(y-2i\right)\left(y+2i\right)$$

9 ga y-2i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$212x+3y=\left(9y-18i\right)\left(y+2i\right)$$

9y-18i ga y+2i ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$212x+3y=9y^{2}+36$$

Ikkala tarafdan 3y ni ayirish.

$$212x=9y^{2}+36-3y$$

Tenglama standart shaklda.

$$212x=9y^{2}-3y+36$$

Ikki tarafini 212 ga bo‘ling.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

212 ga bo'lish 212 ga ko'paytirishni bekor qiladi.

$$x=\frac{9y^{2}-3y+36}{212}$$

9y^{2}+36-3y ni 212 ga bo'lish.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

x uchun yechish

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini y^{2}+4 ga ko'paytirish.

$$212x+3y=9\left(y^{2}+4\right)$$

9 ga y^{2}+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$212x+3y=9y^{2}+36$$

Ikkala tarafdan 3y ni ayirish.

$$212x=9y^{2}+36-3y$$

Tenglama standart shaklda.

$$212x=9y^{2}-3y+36$$

Ikki tarafini 212 ga bo‘ling.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

212 ga bo'lish 212 ga ko'paytirishni bekor qiladi.

$$x=\frac{9y^{2}-3y+36}{212}$$

9y^{2}+36-3y ni 212 ga bo'lish.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

y uchun yechish (complex solution)

$$\left\{\begin{matrix}\\y=\frac{\sqrt{848x-143}+1}{6}\text{, }&\text{unconditionally}\\y=\frac{-\sqrt{848x-143}+1}{6}\text{, }&x\neq \frac{3}{106}i\text{ and }x\neq -\frac{3}{106}i\end{matrix}\right,$$

y uchun yechish

$$y=\frac{-\sqrt{848x-143}+1}{6}$$

$$y=\frac{\sqrt{848x-143}+1}{6}\text{, }x\geq \frac{143}{848}$$