left(x-2right)^2+left(x-1right)^2+x^2=left(x+1right)^2+{left(x+2right)}^2 eching

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

x uchun yechish

$$x=12$$

$$x=0$$

Faktorlash qadamlari

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

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

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

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

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

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

-6x ni olish uchun -4x va -2x ni birlashtirish.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

5 olish uchun 4 va 1'ni qo'shing.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

3x^{2} ni olish uchun 2x^{2} va x^{2} ni birlashtirish.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

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

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

6x ni olish uchun 2x va 4x ni birlashtirish.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

5 olish uchun 1 va 4'ni qo'shing.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

x^{2} ni olish uchun 3x^{2} va -2x^{2} ni birlashtirish.

$$x^{2}-6x+5=6x+5$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}-6x+5-6x=5$$

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

$$x^{2}-12x+5=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}-12x+5-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

$$x^{2}-12x=0$$

x omili.

$$x\left(x-12\right)=0$$

Tenglamani yechish uchun x=0 va x-12=0 ni yeching.

$$x=0 x=12$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

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

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

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

-6x ni olish uchun -4x va -2x ni birlashtirish.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

5 olish uchun 4 va 1'ni qo'shing.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

3x^{2} ni olish uchun 2x^{2} va x^{2} ni birlashtirish.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

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

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

6x ni olish uchun 2x va 4x ni birlashtirish.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

5 olish uchun 1 va 4'ni qo'shing.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

x^{2} ni olish uchun 3x^{2} va -2x^{2} ni birlashtirish.

$$x^{2}-6x+5=6x+5$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}-6x+5-6x=5$$

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

$$x^{2}-12x+5=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}-12x+5-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

$$x^{2}-12x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2}$$

\left(-12\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±12}{2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±12}{2}$$

x=\frac{12±12}{2} tenglamasini yeching, bunda ± musbat. 12 ni 12 ga qo'shish.

$$x=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$x=12$$

x=\frac{12±12}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 12 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=12 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

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

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

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

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

-6x ni olish uchun -4x va -2x ni birlashtirish.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

5 olish uchun 4 va 1'ni qo'shing.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

3x^{2} ni olish uchun 2x^{2} va x^{2} ni birlashtirish.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

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

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

6x ni olish uchun 2x va 4x ni birlashtirish.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

5 olish uchun 1 va 4'ni qo'shing.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

x^{2} ni olish uchun 3x^{2} va -2x^{2} ni birlashtirish.

$$x^{2}-6x+5=6x+5$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}-6x+5-6x=5$$

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

$$x^{2}-12x+5=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}-12x+5-5=0$$

0 olish uchun 5 dan 5 ni ayirish.

$$x^{2}-12x=0$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

-6 kvadratini chiqarish.

$$x^{2}-12x+36=36$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$x-6=6 x-6=-6$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=12 x=0$$