m^2-2m+5=0 eching

$${ m }^{ 2 } -2m+5 = 0$$

m uchun yechish

$$m=1+2i$$

$$m=1-2i$$

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.

$$m^{2}-2m+5=0$$

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 5 ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni 5 marotabaga ko'paytirish.

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

4 ni -20 ga qo'shish.

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

-16 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-2\right)±4i}{2}$$

-2 ning teskarisi 2 ga teng.

$$m=\frac{2±4i}{2}$$

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

$$m=\frac{2+4i}{2}$$

2+4i ni 2 ga bo'lish.

$$m=1+2i$$

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

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

2-4i ni 2 ga bo'lish.

$$m=1-2i$$

Tenglama yechildi.

$$m=1+2i m=1-2i$$

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.

$$m^{2}-2m+5=0$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$m^{2}-2m+5-5=-5$$

O‘zidan 5 ayirilsa 0 qoladi.

$$m^{2}-2m=-5$$

-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.

$$m^{2}-2m+1=-5+1$$

-5 ni 1 ga qo'shish.

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

m^{2}-2m+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.

$$\left(m-1\right)^{2}=-4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-1\right)^{2}}=\sqrt{-4}$$

Qisqartirish.

$$m-1=2i m-1=-2i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$m=1+2i m=1-2i$$