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

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

x uchun yechish

$$x=0$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2\left(3x+1\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

2 ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(6x+2\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

6x+2 ga 3x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$18x^{2}-2+\left(x-2\right)^{2}=2-4x$$

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

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

19x^{2} ni olish uchun 18x^{2} va x^{2} ni birlashtirish.

$$19x^{2}-2-4x+4=2-4x$$

2 olish uchun -2 va 4'ni qo'shing.

$$19x^{2}+2-4x=2-4x$$

4x ni ikki tarafga qo’shing.

$$19x^{2}+2-4x+4x=2$$

0 ni olish uchun -4x va 4x ni birlashtirish.

$$19x^{2}+2=2$$

Ikkala tarafdan 2 ni ayirish.

$$19x^{2}=2-2$$

0 olish uchun 2 dan 2 ni ayirish.

$$19x^{2}=0$$

Ikki tarafini 19 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=0 x=0$$

Tenglama yechildi. Yechimlar bir xil.

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2\left(3x+1\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

2 ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(6x+2\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

6x+2 ga 3x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$18x^{2}-2+\left(x-2\right)^{2}=2-4x$$

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

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

19x^{2} ni olish uchun 18x^{2} va x^{2} ni birlashtirish.

$$19x^{2}-2-4x+4=2-4x$$

2 olish uchun -2 va 4'ni qo'shing.

$$19x^{2}+2-4x=2-4x$$

Ikkala tarafdan 2 ni ayirish.

$$19x^{2}+2-4x-2=-4x$$

0 olish uchun 2 dan 2 ni ayirish.

$$19x^{2}-4x=-4x$$

4x ni ikki tarafga qo’shing.

$$19x^{2}-4x+4x=0$$

0 ni olish uchun -4x va 4x ni birlashtirish.

$$19x^{2}=0$$

Ikki tarafini 19 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

0^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{0±0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$