y^2-2xy+9=0 eching

$$y ^ { 2 } - 2 x y + 9 = 0$$

x uchun yechish

$$x=\frac{y}{2}+\frac{9}{2y}$$

$$y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-2xy+9=-y^{2}$$

Ikkala tarafdan 9 ni ayirish.

$$-2xy=-y^{2}-9$$

Tenglama standart shaklda.

$$\left(-2y\right)x=-y^{2}-9$$

Ikki tarafini -2y ga bo‘ling.

$$\frac{\left(-2y\right)x}{-2y}=\frac{-y^{2}-9}{-2y}$$

-2y ga bo'lish -2y ga ko'paytirishni bekor qiladi.

$$x=\frac{-y^{2}-9}{-2y}$$

-y^{2}-9 ni -2y ga bo'lish.

$$x=\frac{y}{2}+\frac{9}{2y}$$

y uchun yechish (complex solution)

$$y=\sqrt{x^{2}-9}+x$$

$$y=-\sqrt{x^{2}-9}+x$$

y uchun yechish

$$y=\sqrt{x^{2}-9}+x$$

$$y=-\sqrt{x^{2}-9}+x\text{, }|x|\geq 3$$