2a-1=(a-2)(a+2) eching

$$2 a - 1 = ( a - 2 ) ( a + 2 )$$

a uchun yechish

$$a=-1$$

$$a=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(a-2\right)\left(a+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$2a-1=a^{2}-4$$

Ikkala tarafdan a^{2} ni ayirish.

$$2a-1-a^{2}=-4$$

4 ni ikki tarafga qo’shing.

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

3 olish uchun -1 va 4'ni qo'shing.

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

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.

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

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 3 ni c bilan almashtiring.

$$a=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

2 kvadratini chiqarish.

$$a=\frac{-2±\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$a=\frac{-2±\sqrt{4+4\times 3}}{2\left(-1\right)}$$

4 ni 3 marotabaga ko'paytirish.

$$a=\frac{-2±\sqrt{4+12}}{2\left(-1\right)}$$

4 ni 12 ga qo'shish.

$$a=\frac{-2±\sqrt{16}}{2\left(-1\right)}$$

16 ning kvadrat ildizini chiqarish.

$$a=\frac{-2±4}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$a=\frac{-2±4}{-2}$$

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

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

2 ni -2 ga bo'lish.

$$a=-1$$

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

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

-6 ni -2 ga bo'lish.

$$a=3$$

Tenglama yechildi.

$$a=-1 a=3$$

Kvadratni yakunlash bo'yicha qadamlar

Hisoblang: \left(a-2\right)\left(a+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$2a-1=a^{2}-4$$

Ikkala tarafdan a^{2} ni ayirish.

$$2a-1-a^{2}=-4$$

1 ni ikki tarafga qo’shing.

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

-3 olish uchun -4 va 1'ni qo'shing.

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

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

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

Ikki tarafini -1 ga bo‘ling.

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

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

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

2 ni -1 ga bo'lish.

$$a^{2}-2a=-\frac{3}{-1}$$

-3 ni -1 ga bo'lish.

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

-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.

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

3 ni 1 ga qo'shish.

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

a^{2}-2a+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.

$$\left(a-1\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$a-1=2 a-1=-2$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$a=3 a=-1$$