y^2-8x+6y+1=0 eching

$$y ^ { 2 } - 8 x + 6 y + 1 = 0$$

x uchun yechish

$$x=\frac{y^{2}+6y+1}{8}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan y^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-8x+6y+1=-y^{2}$$

Ikkala tarafdan 6y ni ayirish.

$$-8x+1=-y^{2}-6y$$

Ikkala tarafdan 1 ni ayirish.

$$-8x=-y^{2}-6y-1$$

Ikki tarafini -8 ga bo‘ling.

$$\frac{-8x}{-8}=\frac{-y^{2}-6y-1}{-8}$$

-8 ga bo'lish -8 ga ko'paytirishni bekor qiladi.

$$x=\frac{-y^{2}-6y-1}{-8}$$

-y^{2}-6y-1 ni -8 ga bo'lish.

$$x=\frac{y^{2}}{8}+\frac{3y}{4}+\frac{1}{8}$$

y uchun yechish (complex solution)

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

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

y uchun yechish

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

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