(x+1)2-(4-2x)=x^2+3 eching

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

x uchun yechish (complex solution)

$$x=2-i$$

$$x=2+i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

4-2x teskarisini topish uchun har birining teskarisini toping.

$$2x+2-4+2x=x^{2}+3$$

-2 olish uchun 2 dan 4 ni ayirish.

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

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

$$4x-2=x^{2}+3$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x-2-x^{2}=3$$

Ikkala tarafdan 3 ni ayirish.

$$4x-2-x^{2}-3=0$$

-5 olish uchun -2 dan 3 ni ayirish.

$$4x-5-x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-x^{2}+4x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 4 ni b va -5 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4\left(-5\right)}}{2\left(-1\right)}$$

4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-20}}{2\left(-1\right)}$$

16 ni -20 ga qo'shish.

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

-4 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±2i}{-2}$$

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

$$x=\frac{-4+2i}{-2}$$

-4+2i ni -2 ga bo'lish.

$$x=2-i$$

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

$$x=\frac{-4-2i}{-2}$$

-4-2i ni -2 ga bo'lish.

$$x=2+i$$

Tenglama yechildi.

$$x=2-i x=2+i$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

4-2x teskarisini topish uchun har birining teskarisini toping.

$$2x+2-4+2x=x^{2}+3$$

-2 olish uchun 2 dan 4 ni ayirish.

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

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

$$4x-2=x^{2}+3$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x-2-x^{2}=3$$

2 ni ikki tarafga qo’shing.

$$4x-x^{2}=3+2$$

5 olish uchun 3 va 2'ni qo'shing.

$$4x-x^{2}=5$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-x^{2}+4x=5$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+4x}{-1}=\frac{5}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{4}{-1}x=\frac{5}{-1}$$

4 ni -1 ga bo'lish.

$$x^{2}-4x=\frac{5}{-1}$$

5 ni -1 ga bo'lish.

$$x^{2}-4x=-5$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-4x+\left(-2\right)^{2}=-5+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=-5+4$$

-5 ni 4 ga qo'shish.

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

x^{2}-4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-2=i x-2=-i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2+i x=2-i$$