(7-x)^2+(1-y)^2=(3-x)^2+(5-y^2) eching

$$( 7 - x ) ^ { 2 } + ( 1 - y ) ^ { 2 } = ( 3 - x ) ^ { 2 } + ( 5 - y ^ { 2 } )$$

x uchun yechish

$$x=\frac{y^{2}-y+18}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(7-x\right)^{2} kengaytirilishi uchun ishlating.

$$49-14x+x^{2}+\left(1-y\right)^{2}=\left(3-x\right)^{2}+5-y^{2}$$

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

$$49-14x+x^{2}+1-2y+y^{2}=\left(3-x\right)^{2}+5-y^{2}$$

50 olish uchun 49 va 1'ni qo'shing.

$$50-14x+x^{2}-2y+y^{2}=\left(3-x\right)^{2}+5-y^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3-x\right)^{2} kengaytirilishi uchun ishlating.

$$50-14x+x^{2}-2y+y^{2}=9-6x+x^{2}+5-y^{2}$$

14 olish uchun 9 va 5'ni qo'shing.

$$50-14x+x^{2}-2y+y^{2}=14-6x+x^{2}-y^{2}$$

6x ni ikki tarafga qo’shing.

$$50-14x+x^{2}-2y+y^{2}+6x=14+x^{2}-y^{2}$$

-8x ni olish uchun -14x va 6x ni birlashtirish.

$$50-8x+x^{2}-2y+y^{2}=14+x^{2}-y^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$50-8x+x^{2}-2y+y^{2}-x^{2}=14-y^{2}$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$50-8x-2y+y^{2}=14-y^{2}$$

Ikkala tarafdan 50 ni ayirish.

$$-8x-2y+y^{2}=14-y^{2}-50$$

-36 olish uchun 14 dan 50 ni ayirish.

$$-8x-2y+y^{2}=-36-y^{2}$$

2y ni ikki tarafga qo’shing.

$$-8x+y^{2}=-36-y^{2}+2y$$

Ikkala tarafdan y^{2} ni ayirish.

$$-8x=-36-y^{2}+2y-y^{2}$$

-2y^{2} ni olish uchun -y^{2} va -y^{2} ni birlashtirish.

$$-8x=-36-2y^{2}+2y$$

Tenglama standart shaklda.

$$-8x=-2y^{2}+2y-36$$

Ikki tarafini -8 ga bo‘ling.

$$\frac{-8x}{-8}=\frac{-2y^{2}+2y-36}{-8}$$

-8 ga bo'lish -8 ga ko'paytirishni bekor qiladi.

$$x=\frac{-2y^{2}+2y-36}{-8}$$

-36-2y^{2}+2y ni -8 ga bo'lish.

$$x=\frac{y^{2}}{4}-\frac{y}{4}+\frac{9}{2}$$

y uchun yechish (complex solution)

$$y=\frac{\sqrt{16x-71}+1}{2}$$

$$y=\frac{-\sqrt{16x-71}+1}{2}$$

y uchun yechish

$$y=\frac{\sqrt{16x-71}+1}{2}$$

$$y=\frac{-\sqrt{16x-71}+1}{2}\text{, }x\geq \frac{71}{16}$$