x^2-2yx-y+1=0 eching

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

y uchun yechish

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

$$x\neq -\frac{1}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-2yx-y+1=-x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$-2yx-y=-x^{2}-1$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-2x-1\right)y=-x^{2}-1$$

Ikki tarafini -2x-1 ga bo‘ling.

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

-2x-1 ga bo'lish -2x-1 ga ko'paytirishni bekor qiladi.

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

-x^{2}-1 ni -2x-1 ga bo'lish.

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

x uchun yechish (complex solution)

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

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

x uchun yechish

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

$$x=-\sqrt{y^{2}+y-1}+y\text{, }y\geq \frac{\sqrt{5}-1}{2}\text{ or }y\leq \frac{-\sqrt{5}-1}{2}$$