left(-3-xright)^2+left(4-yright)^2=left(6-xright)^2+left(2-yright)^2 eching

$${ \left(-3-x \right) }^{ 2 } + { \left(4-y \right) }^{ 2 } = { \left(6-x \right) }^{ 2 } + { \left(2-y \right) }^{ 2 }$$

x uchun yechish

$$x=\frac{2y}{9}+\frac{5}{6}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$9+6x+x^{2}+\left(4-y\right)^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-y\right)^{2} kengaytirilishi uchun ishlating.

$$9+6x+x^{2}+16-8y+y^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

25 olish uchun 9 va 16'ni qo'shing.

$$25+6x+x^{2}-8y+y^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(6-x\right)^{2} kengaytirilishi uchun ishlating.

$$25+6x+x^{2}-8y+y^{2}=36-12x+x^{2}+\left(2-y\right)^{2}$$

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

$$25+6x+x^{2}-8y+y^{2}=36-12x+x^{2}+4-4y+y^{2}$$

40 olish uchun 36 va 4'ni qo'shing.

$$25+6x+x^{2}-8y+y^{2}=40-12x+x^{2}-4y+y^{2}$$

12x ni ikki tarafga qo’shing.

$$25+6x+x^{2}-8y+y^{2}+12x=40+x^{2}-4y+y^{2}$$

18x ni olish uchun 6x va 12x ni birlashtirish.

$$25+18x+x^{2}-8y+y^{2}=40+x^{2}-4y+y^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$25+18x+x^{2}-8y+y^{2}-x^{2}=40-4y+y^{2}$$

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

$$25+18x-8y+y^{2}=40-4y+y^{2}$$

Ikkala tarafdan 25 ni ayirish.

$$18x-8y+y^{2}=40-4y+y^{2}-25$$

15 olish uchun 40 dan 25 ni ayirish.

$$18x-8y+y^{2}=15-4y+y^{2}$$

8y ni ikki tarafga qo’shing.

$$18x+y^{2}=15-4y+y^{2}+8y$$

4y ni olish uchun -4y va 8y ni birlashtirish.

$$18x+y^{2}=15+4y+y^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$18x=15+4y+y^{2}-y^{2}$$

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

$$18x=15+4y$$

Tenglama standart shaklda.

$$18x=4y+15$$

Ikki tarafini 18 ga bo‘ling.

$$\frac{18x}{18}=\frac{4y+15}{18}$$

18 ga bo'lish 18 ga ko'paytirishni bekor qiladi.

$$x=\frac{4y+15}{18}$$

15+4y ni 18 ga bo'lish.

$$x=\frac{2y}{9}+\frac{5}{6}$$

y uchun yechish

$$y=\frac{9x}{2}-\frac{15}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$9+6x+x^{2}+\left(4-y\right)^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-y\right)^{2} kengaytirilishi uchun ishlating.

$$9+6x+x^{2}+16-8y+y^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

25 olish uchun 9 va 16'ni qo'shing.

$$25+6x+x^{2}-8y+y^{2}=\left(6-x\right)^{2}+\left(2-y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(6-x\right)^{2} kengaytirilishi uchun ishlating.

$$25+6x+x^{2}-8y+y^{2}=36-12x+x^{2}+\left(2-y\right)^{2}$$

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

$$25+6x+x^{2}-8y+y^{2}=36-12x+x^{2}+4-4y+y^{2}$$

40 olish uchun 36 va 4'ni qo'shing.

$$25+6x+x^{2}-8y+y^{2}=40-12x+x^{2}-4y+y^{2}$$

4y ni ikki tarafga qo’shing.

$$25+6x+x^{2}-8y+y^{2}+4y=40-12x+x^{2}+y^{2}$$

-4y ni olish uchun -8y va 4y ni birlashtirish.

$$25+6x+x^{2}-4y+y^{2}=40-12x+x^{2}+y^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$25+6x+x^{2}-4y+y^{2}-y^{2}=40-12x+x^{2}$$

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

$$25+6x+x^{2}-4y=40-12x+x^{2}$$

Ikkala tarafdan 25 ni ayirish.

$$6x+x^{2}-4y=40-12x+x^{2}-25$$

15 olish uchun 40 dan 25 ni ayirish.

$$6x+x^{2}-4y=15-12x+x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}-4y=15-12x+x^{2}-6x$$

-18x ni olish uchun -12x va -6x ni birlashtirish.

$$x^{2}-4y=15-18x+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-4y=15-18x+x^{2}-x^{2}$$

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

$$-4y=15-18x$$

Ikki tarafini -4 ga bo‘ling.

$$\frac{-4y}{-4}=\frac{15-18x}{-4}$$

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

$$y=\frac{15-18x}{-4}$$

15-18x ni -4 ga bo'lish.

$$y=\frac{9x}{2}-\frac{15}{4}$$