a^2+2=a-4 eching

$$a ^ { 2 } + 2 = a - 4$$

a uchun yechish

$$a=\frac{1+\sqrt{23}i}{2}\approx 0,5+2,397915762i$$

$$a=\frac{-\sqrt{23}i+1}{2}\approx 0,5-2,397915762i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan a ni ayirish.

$$a^{2}+2-a=-4$$

4 ni ikki tarafga qo’shing.

$$a^{2}+2-a+4=0$$

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

$$a^{2}+6-a=0$$

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.

$$a^{2}-a+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va 6 ni c bilan almashtiring.

$$a=\frac{-\left(-1\right)±\sqrt{1-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$a=\frac{-\left(-1\right)±\sqrt{1-24}}{2}$$

1 ni -24 ga qo'shish.

$$a=\frac{-\left(-1\right)±\sqrt{-23}}{2}$$

-23 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-1\right)±\sqrt{23}i}{2}$$

-1 ning teskarisi 1 ga teng.

$$a=\frac{1±\sqrt{23}i}{2}$$

a=\frac{1±\sqrt{23}i}{2} tenglamasini yeching, bunda ± musbat. 1 ni i\sqrt{23} ga qo'shish.

$$a=\frac{1+\sqrt{23}i}{2}$$

a=\frac{1±\sqrt{23}i}{2} tenglamasini yeching, bunda ± manfiy. 1 dan i\sqrt{23} ni ayirish.

$$a=\frac{-\sqrt{23}i+1}{2}$$

Tenglama yechildi.

$$a=\frac{1+\sqrt{23}i}{2} a=\frac{-\sqrt{23}i+1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan a ni ayirish.

$$a^{2}+2-a=-4$$

Ikkala tarafdan 2 ni ayirish.

$$a^{2}-a=-4-2$$

-6 olish uchun -4 dan 2 ni ayirish.

$$a^{2}-a=-6$$

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

$$a^{2}-a+\left(-\frac{1}{2}\right)^{2}=-6+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$a^{2}-a+\frac{1}{4}=-6+\frac{1}{4}$$

-6 ni \frac{1}{4} ga qo'shish.

$$a^{2}-a+\frac{1}{4}=-\frac{23}{4}$$

a^{2}-a+\frac{1}{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.

$$\left(a-\frac{1}{2}\right)^{2}=-\frac{23}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{23}{4}}$$

Qisqartirish.

$$a-\frac{1}{2}=\frac{\sqrt{23}i}{2} a-\frac{1}{2}=-\frac{\sqrt{23}i}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$a=\frac{1+\sqrt{23}i}{2} a=\frac{-\sqrt{23}i+1}{2}$$