3a+(a^2+1)=1 eching

$$3 a + ( a ^ { 2 } + 1 ) = 1$$

a uchun yechish

$$a=-3$$

$$a=0$$

Faktorlash qadamlari

Ikkala tarafdan 1 ni ayirish.

$$3a+a^{2}+1-1=0$$

0 olish uchun 1 dan 1 ni ayirish.

$$3a+a^{2}=0$$

a omili.

$$a\left(3+a\right)=0$$

Tenglamani yechish uchun a=0 va 3+a=0 ni yeching.

$$a=0 a=-3$$

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.

$$a^{2}+3a+1=1$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$a^{2}+3a+1-1=1-1$$

O‘zidan 1 ayirilsa 0 qoladi.

$$a^{2}+3a+1-1=0$$

1 dan 1 ni ayirish.

$$a^{2}+3a=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 3 ni b va 0 ni c bilan almashtiring.

$$a=\frac{-3±\sqrt{3^{2}}}{2}$$

3^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-3±3}{2}$$

a=\frac{-3±3}{2} tenglamasini yeching, bunda ± musbat. -3 ni 3 ga qo'shish.

$$a=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$a=0$$

a=\frac{-3±3}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 3 ni ayirish.

$$a=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$a=-3$$

Tenglama yechildi.

$$a=0 a=-3$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 1 ni ayirish.

$$3a+a^{2}+1-1=0$$

0 olish uchun 1 dan 1 ni ayirish.

$$3a+a^{2}=0$$

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

$$a^{2}+3a=0$$

3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}+3a+\left(\frac{3}{2}\right)^{2}=\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$a^{2}+3a+\frac{9}{4}=\frac{9}{4}$$

a^{2}+3a+\frac{9}{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.

$$\left(a+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$a+\frac{3}{2}=\frac{3}{2} a+\frac{3}{2}=-\frac{3}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$a=0 a=-3$$