a^2+4a^2+2a+1=0 eching

$$a ^ { 2 } + 4 a ^ { 2 } + 2 a + 1 = 0$$

a uchun yechish

$$a=-\frac{1}{5}+\frac{2}{5}i=-0,2+0,4i$$

$$a=-\frac{1}{5}-\frac{2}{5}i=-0,2-0,4i$$

Kvadrat tenglamalaridan foydalanish qoidalari

5a^{2} ni olish uchun a^{2} va 4a^{2} ni birlashtirish.

$$5a^{2}+2a+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 2 ni b va 1 ni c bilan almashtiring.

$$a=\frac{-2±\sqrt{2^{2}-4\times 5}}{2\times 5}$$

2 kvadratini chiqarish.

$$a=\frac{-2±\sqrt{4-4\times 5}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$a=\frac{-2±\sqrt{4-20}}{2\times 5}$$

4 ni -20 ga qo'shish.

$$a=\frac{-2±\sqrt{-16}}{2\times 5}$$

-16 ning kvadrat ildizini chiqarish.

$$a=\frac{-2±4i}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$a=\frac{-2±4i}{10}$$

a=\frac{-2±4i}{10} tenglamasini yeching, bunda ± musbat. -2 ni 4i ga qo'shish.

$$a=\frac{-2+4i}{10}$$

-2+4i ni 10 ga bo'lish.

$$a=-\frac{1}{5}+\frac{2}{5}i$$

a=\frac{-2±4i}{10} tenglamasini yeching, bunda ± manfiy. -2 dan 4i ni ayirish.

$$a=\frac{-2-4i}{10}$$

-2-4i ni 10 ga bo'lish.

$$a=-\frac{1}{5}-\frac{2}{5}i$$

Tenglama yechildi.

$$a=-\frac{1}{5}+\frac{2}{5}i a=-\frac{1}{5}-\frac{2}{5}i$$

Kvadratni yakunlash bo'yicha qadamlar

5a^{2} ni olish uchun a^{2} va 4a^{2} ni birlashtirish.

$$5a^{2}+2a+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikki tarafini 5 ga bo‘ling.

$$\frac{5a^{2}+2a}{5}=-\frac{1}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$a^{2}+\frac{2}{5}a=-\frac{1}{5}$$

\frac{2}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{5} olish uchun. Keyin, \frac{1}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}+\frac{2}{5}a+\left(\frac{1}{5}\right)^{2}=-\frac{1}{5}+\left(\frac{1}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{5} kvadratini chiqarish.

$$a^{2}+\frac{2}{5}a+\frac{1}{25}=-\frac{1}{5}+\frac{1}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{5} ni \frac{1}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$a^{2}+\frac{2}{5}a+\frac{1}{25}=-\frac{4}{25}$$

a^{2}+\frac{2}{5}a+\frac{1}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a+\frac{1}{5}\right)^{2}=-\frac{4}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+\frac{1}{5}\right)^{2}}=\sqrt{-\frac{4}{25}}$$

Qisqartirish.

$$a+\frac{1}{5}=\frac{2}{5}i a+\frac{1}{5}=-\frac{2}{5}i$$

Tenglamaning ikkala tarafidan \frac{1}{5} ni ayirish.

$$a=-\frac{1}{5}+\frac{2}{5}i a=-\frac{1}{5}-\frac{2}{5}i$$