(x+1)y^2=12 eching

$$( x + 1 ) y ^ { 2 } = 12$$

x uchun yechish

$$x=-1+\frac{12}{y^{2}}$$

$$y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+1 ga y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$xy^{2}+y^{2}=12$$

Ikkala tarafdan y^{2} ni ayirish.

$$xy^{2}=12-y^{2}$$

Tenglama standart shaklda.

$$y^{2}x=12-y^{2}$$

Ikki tarafini y^{2} ga bo‘ling.

$$\frac{y^{2}x}{y^{2}}=\frac{12-y^{2}}{y^{2}}$$

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

$$x=\frac{12-y^{2}}{y^{2}}$$

12-y^{2} ni y^{2} ga bo'lish.

$$x=-1+\frac{12}{y^{2}}$$

y uchun yechish (complex solution)

$$y=-2\sqrt{3}\left(x+1\right)^{-\frac{1}{2}}$$

$$y=2\sqrt{3}\left(x+1\right)^{-\frac{1}{2}}\text{, }x\neq -1$$

y uchun yechish

$$y=2\sqrt{\frac{3}{x+1}}$$

$$y=-2\sqrt{\frac{3}{x+1}}\text{, }x>-1$$