(x+1)^2=2x+1 eching

$$( x + 1 ) ^ { 2 } = 2 x + 1$$

x uchun yechish

$$x=0$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$x^{2}+2x+1=2x+1$$

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+2x+1-2x=1$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$x^{2}+1=1$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}=1-1$$

0 olish uchun 1 dan 1 ni ayirish.

$$x^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=0 x=0$$

Tenglama yechildi. Yechimlar bir xil.

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+2x+1=2x+1$$

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+2x+1-2x=1$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$x^{2}+1=1$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}+1-1=0$$

0 olish uchun 1 dan 1 ni ayirish.

$$x^{2}=0$$

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.

$$x=0$$