(x-1)^2=-y+10/3 eching

$$( x - 1 ) ^ { 2 } = - y + \frac { 10 } { 3 }$$

y uchun yechish

$$y=-\left(x-1\right)^{2}+\frac{10}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-2x+1=-y+\frac{10}{3}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-y+\frac{10}{3}=x^{2}-2x+1$$

Ikkala tarafdan \frac{10}{3} ni ayirish.

$$-y=x^{2}-2x+1-\frac{10}{3}$$

-\frac{7}{3} olish uchun 1 dan \frac{10}{3} ni ayirish.

$$-y=x^{2}-2x-\frac{7}{3}$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-y}{-1}=\frac{x^{2}-2x-\frac{7}{3}}{-1}$$

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

$$y=\frac{x^{2}-2x-\frac{7}{3}}{-1}$$

x^{2}-2x-\frac{7}{3} ni -1 ga bo'lish.

$$y=\frac{7}{3}+2x-x^{2}$$

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

$$x=\frac{\sqrt{30-9y}}{3}+1$$

x uchun yechish

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

$$x=\frac{\sqrt{30-9y}}{3}+1\text{, }y\leq \frac{10}{3}$$