x^2-4x+5=0 eching

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

x uchun yechish (complex solution)

$$x=2+i$$

$$x=2-i$$

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.

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

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.

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

-4 kvadratini chiqarish.

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

-4 ni 5 marotabaga ko'paytirish.

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

16 ni -20 ga qo'shish.

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

-4 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2i}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2i}{2}$$

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

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

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

Tenglamaning ikkala tarafidan 5 ni ayirish.

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

O‘zidan 5 ayirilsa 0 qoladi.

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

-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.

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