x^2=2x+1 eching

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

x uchun yechish

$$x=\sqrt{2}+1\approx 2,414213562$$

$$x=1-\sqrt{2}\approx -0,414213562$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

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

Ikkala tarafdan 1 ni ayirish.

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

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

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4}}{2}$$

4 ni 4 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{2}}{2}$$

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

$$x=\frac{2\sqrt{2}+2}{2}$$

2+2\sqrt{2} ni 2 ga bo'lish.

$$x=\sqrt{2}+1$$

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

$$x=\frac{2-2\sqrt{2}}{2}$$

2-2\sqrt{2} ni 2 ga bo'lish.

$$x=1-\sqrt{2}$$

Tenglama yechildi.

$$x=\sqrt{2}+1 x=1-\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

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

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

1 ni 1 ga qo'shish.

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

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-1=\sqrt{2} x-1=-\sqrt{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{2}+1 x=1-\sqrt{2}$$