x uchun yechish (complex solution)
x=1+i
x=1-i
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Baham ko'rish
Klipbordga nusxa olish
x^{2}-2x+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=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2}}{2}
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 2 ni c bilan almashtiring.
x=\frac{-\left(-2\right)±\sqrt{4-4\times 2}}{2}
-2 kvadratini chiqarish.
x=\frac{-\left(-2\right)±\sqrt{4-8}}{2}
-4 ni 2 marotabaga ko'paytirish.
x=\frac{-\left(-2\right)±\sqrt{-4}}{2}
4 ni -8 ga qo'shish.
x=\frac{-\left(-2\right)±2i}{2}
-4 ning kvadrat ildizini chiqarish.
x=\frac{2±2i}{2}
-2 ning teskarisi 2 ga teng.
x=\frac{2+2i}{2}
x=\frac{2±2i}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2i ga qo'shish.
x=1+i
2+2i ni 2 ga bo'lish.
x=\frac{2-2i}{2}
x=\frac{2±2i}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2i ni ayirish.
x=1-i
2-2i ni 2 ga bo'lish.
x=1+i x=1-i
Tenglama yechildi.
x^{2}-2x+2=0
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+2-2=-2
Tenglamaning ikkala tarafidan 2 ni ayirish.
x^{2}-2x=-2
O‘zidan 2 ayirilsa 0 qoladi.
x^{2}-2x+1=-2+1
-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=-1
-2 ni 1 ga qo'shish.
\left(x-1\right)^{2}=-1
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.
\sqrt{\left(x-1\right)^{2}}=\sqrt{-1}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-1=i x-1=-i
Qisqartirish.
x=1+i x=1-i
1 ni tenglamaning ikkala tarafiga qo'shish.
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