x^2-2x+4=0 eching

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

x uchun yechish (complex solution)

$$x=1+\sqrt{3}i\approx 1+1,732050808i$$

$$x=-\sqrt{3}i+1\approx 1-1,732050808i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

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

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 4 ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

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

4 ni -16 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{-12}}{2}$$

-12 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{3}i}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{3}i}{2}$$

x=\frac{2±2\sqrt{3}i}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2i\sqrt{3} ga qo'shish.

$$x=\frac{2+2\sqrt{3}i}{2}$$

2+2i\sqrt{3} ni 2 ga bo'lish.

$$x=1+\sqrt{3}i$$

x=\frac{2±2\sqrt{3}i}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2i\sqrt{3} ni ayirish.

$$x=\frac{-2\sqrt{3}i+2}{2}$$

2-2i\sqrt{3} ni 2 ga bo'lish.

$$x=-\sqrt{3}i+1$$

Tenglama yechildi.

$$x=1+\sqrt{3}i x=-\sqrt{3}i+1$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

Tenglamaning ikkala tarafidan 4 ni ayirish.

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

O‘zidan 4 ayirilsa 0 qoladi.

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

-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.

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

-4 ni 1 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-1=\sqrt{3}i x-1=-\sqrt{3}i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1+\sqrt{3}i x=-\sqrt{3}i+1$$