16x^2-64x+65=0 eching

$$16 x ^ { 2 } - 64 x + 65 = 0$$

x uchun yechish (complex solution)

$$x=2+\frac{1}{4}i=2+0,25i$$

$$x=2-\frac{1}{4}i=2-0,25i$$

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.

$$16x^{2}-64x+65=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, -64 ni b va 65 ni c bilan almashtiring.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 16\times 65}}{2\times 16}$$

-64 kvadratini chiqarish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\times 16\times 65}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-64\times 65}}{2\times 16}$$

-64 ni 65 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4160}}{2\times 16}$$

4096 ni -4160 ga qo'shish.

$$x=\frac{-\left(-64\right)±\sqrt{-64}}{2\times 16}$$

-64 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-64\right)±8i}{2\times 16}$$

-64 ning teskarisi 64 ga teng.

$$x=\frac{64±8i}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{64±8i}{32}$$

x=\frac{64±8i}{32} tenglamasini yeching, bunda ± musbat. 64 ni 8i ga qo'shish.

$$x=\frac{64+8i}{32}$$

64+8i ni 32 ga bo'lish.

$$x=2+\frac{1}{4}i$$

x=\frac{64±8i}{32} tenglamasini yeching, bunda ± manfiy. 64 dan 8i ni ayirish.

$$x=\frac{64-8i}{32}$$

64-8i ni 32 ga bo'lish.

$$x=2-\frac{1}{4}i$$

Tenglama yechildi.

$$x=2+\frac{1}{4}i x=2-\frac{1}{4}i$$

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.

$$16x^{2}-64x+65=0$$

Tenglamaning ikkala tarafidan 65 ni ayirish.

$$16x^{2}-64x+65-65=-65$$

O‘zidan 65 ayirilsa 0 qoladi.

$$16x^{2}-64x=-65$$

Ikki tarafini 16 ga bo‘ling.

$$\frac{16x^{2}-64x}{16}=-\frac{65}{16}$$

16 ga bo'lish 16 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{64}{16}\right)x=-\frac{65}{16}$$

-64 ni 16 ga bo'lish.

$$x^{2}-4x=-\frac{65}{16}$$

-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.

$$x^{2}-4x+\left(-2\right)^{2}=-\frac{65}{16}+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=-\frac{65}{16}+4$$

-\frac{65}{16} ni 4 ga qo'shish.

$$x^{2}-4x+4=-\frac{1}{16}$$

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.

$$\left(x-2\right)^{2}=-\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{-\frac{1}{16}}$$

Qisqartirish.

$$x-2=\frac{1}{4}i x-2=-\frac{1}{4}i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2+\frac{1}{4}i x=2-\frac{1}{4}i$$