2y^2-4x+1=0 eching

$$2 y ^ { 2 } - 4 x + 1 = 0$$

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-4x+1=-2y^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$-4x=-2y^{2}-1$$

Ikki tarafini -4 ga bo‘ling.

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

-4 ga bo'lish -4 ga ko'paytirishni bekor qiladi.

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

-2y^{2}-1 ni -4 ga bo'lish.

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

y uchun yechish (complex solution)

$$y=-\frac{\sqrt{8x-2}}{2}$$

$$y=\frac{\sqrt{8x-2}}{2}$$

y uchun yechish

$$y=\frac{\sqrt{8x-2}}{2}$$

$$y=-\frac{\sqrt{8x-2}}{2}\text{, }x\geq \frac{1}{4}$$