a^2-3a=0 eching

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

a uchun yechish

$$a=3$$

$$a=0$$

Faktorlash qadamlari

a omili.

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

Tenglamani yechish uchun a=0 va a-3=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.

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

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.

$$a=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2}$$

\left(-3\right)^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-3\right)±3}{2}$$

-3 ning teskarisi 3 ga teng.

$$a=\frac{3±3}{2}$$

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

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

6 ni 2 ga bo'lish.

$$a=3$$

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

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

0 ni 2 ga bo'lish.

$$a=0$$

Tenglama yechildi.

$$a=3 a=0$$

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.

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

-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.

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

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$a=3 a=0$$