2x^2-xy-y=0 eching

$$2 { x }^{ 2 } -xy-y=0$$

y uchun yechish

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

$$x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini -x-1 ga bo‘ling.

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

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

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

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

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

x uchun yechish (complex solution)

$$x=\frac{\sqrt{y\left(y+8\right)}+y}{4}$$

$$x=\frac{-\sqrt{y\left(y+8\right)}+y}{4}$$

x uchun yechish

$$x=\frac{\sqrt{y\left(y+8\right)}+y}{4}$$

$$x=\frac{-\sqrt{y\left(y+8\right)}+y}{4}\text{, }y\leq -8\text{ or }y\geq 0$$