x^2-x-y=0 eching

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

y uchun yechish

$$y=x\left(x-1\right)$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

x ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

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

Ikki tarafini -1 ga bo‘ling.

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

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

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

x\left(1-x\right) ni -1 ga bo'lish.

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

x uchun yechish (complex solution)

$$x=\frac{\sqrt{4y+1}+1}{2}$$

$$x=\frac{-\sqrt{4y+1}+1}{2}$$

x uchun yechish

$$x=\frac{\sqrt{4y+1}+1}{2}$$

$$x=\frac{-\sqrt{4y+1}+1}{2}\text{, }y\geq -\frac{1}{4}$$