x^2=-x^2+4x+1 eching

$$x ^ { 2 } = - x ^ { 2 } + 4 x + 1$$

x uchun yechish

$$x=\frac{\sqrt{6}}{2}+1\approx 2,224744871$$

$$x=-\frac{\sqrt{6}}{2}+1\approx -0,224744871$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} ni ikki tarafga qo’shing.

$$x^{2}+x^{2}=4x+1$$

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

$$2x^{2}=4x+1$$

Ikkala tarafdan 4x ni ayirish.

$$2x^{2}-4x=1$$

Ikkala tarafdan 1 ni ayirish.

$$2x^{2}-4x-1=0$$

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

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

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-1\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-1\right)}}{2\times 2}$$

-8 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+8}}{2\times 2}$$

16 ni 8 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{24}}{2\times 2}$$

24 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{6}}{2\times 2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{6}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{6}}{4}$$

x=\frac{4±2\sqrt{6}}{4} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{6} ga qo'shish.

$$x=\frac{2\sqrt{6}+4}{4}$$

4+2\sqrt{6} ni 4 ga bo'lish.

$$x=\frac{\sqrt{6}}{2}+1$$

x=\frac{4±2\sqrt{6}}{4} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{6} ni ayirish.

$$x=\frac{4-2\sqrt{6}}{4}$$

4-2\sqrt{6} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{6}}{2}+1$$

Tenglama yechildi.

$$x=\frac{\sqrt{6}}{2}+1 x=-\frac{\sqrt{6}}{2}+1$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} ni ikki tarafga qo’shing.

$$x^{2}+x^{2}=4x+1$$

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

$$2x^{2}=4x+1$$

Ikkala tarafdan 4x ni ayirish.

$$2x^{2}-4x=1$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-4x}{2}=\frac{1}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

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

-4 ni 2 ga bo'lish.

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

-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.

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

\frac{1}{2} ni 1 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{3}{2}}$$

Qisqartirish.

$$x-1=\frac{\sqrt{6}}{2} x-1=-\frac{\sqrt{6}}{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{6}}{2}+1 x=-\frac{\sqrt{6}}{2}+1$$