3x^2+ax+7=3(x-2)^2+b eching

$$3 x ^ { 2 } + a x + 7 = 3 ( x - 2 ) ^ { 2 } + b$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{5+b-12x}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=-5\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

3 ga x^{2}-4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$ax+7=3x^{2}-12x+12+b-3x^{2}$$

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$ax+7=-12x+12+b$$

Ikkala tarafdan 7 ni ayirish.

$$ax=-12x+12+b-7$$

5 olish uchun 12 dan 7 ni ayirish.

$$ax=-12x+5+b$$

Tenglama standart shaklda.

$$xa=5+b-12x$$

Ikki tarafini x ga bo‘ling.

$$\frac{xa}{x}=\frac{5+b-12x}{x}$$

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

$$a=\frac{5+b-12x}{x}$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{5+b-12x}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=-5\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

3 ga x^{2}-4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$ax+7=3x^{2}-12x+12+b-3x^{2}$$

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$ax+7=-12x+12+b$$

Ikkala tarafdan 7 ni ayirish.

$$ax=-12x+12+b-7$$

5 olish uchun 12 dan 7 ni ayirish.

$$ax=-12x+5+b$$

Tenglama standart shaklda.

$$xa=5+b-12x$$

Ikki tarafini x ga bo‘ling.

$$\frac{xa}{x}=\frac{5+b-12x}{x}$$

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

$$a=\frac{5+b-12x}{x}$$

b uchun yechish

$$b=ax+12x-5$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

3 ga x^{2}-4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3x^{2}-12x+12+b=3x^{2}+ax+7$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$-12x+12+b=3x^{2}+ax+7-3x^{2}$$

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$-12x+12+b=ax+7$$

12x ni ikki tarafga qo’shing.

$$12+b=ax+7+12x$$

Ikkala tarafdan 12 ni ayirish.

$$b=ax+7+12x-12$$

-5 olish uchun 7 dan 12 ni ayirish.

$$b=ax-5+12x$$