(y-2)^2=4(x-1) eching

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

x uchun yechish

$$x=\frac{\left(y-2\right)^{2}+4}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(y-2\right)^{2} kengaytirilishi uchun ishlating.

$$y^{2}-4y+4=4\left(x-1\right)$$

4 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

4 ni ikki tarafga qo’shing.

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

8 olish uchun 4 va 4'ni qo'shing.

$$4x=y^{2}-4y+8$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x}{4}=\frac{y^{2}-4y+8}{4}$$

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

$$x=\frac{y^{2}-4y+8}{4}$$

y^{2}-4y+8 ni 4 ga bo'lish.

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

y uchun yechish (complex solution)

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

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

y uchun yechish

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

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