8x^2+36+47=2Ax^2+7Ax+6A+6Bx+9B+3x^2+5x-2 eching

$$8 x ^ { 2 } + 36 + 47 = 2 A x ^ { 2 } + 7 A x + 6 A + 6 B x + 9 B + 3 x ^ { 2 } + 5 x - 2$$

A uchun yechish (complex solution)

$$\left\{\begin{matrix}A=-\frac{-5x^{2}+6Bx+5x+9B-85}{\left(x+2\right)\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }x\neq -2\\A\in \mathrm{C}\text{, }&x=-2\text{ and }B=-\frac{115}{3}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

83 olish uchun 36 va 47'ni qo'shing.

$$8x^{2}+83=2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2=8x^{2}+83$$

Ikkala tarafdan 6Bx ni ayirish.

$$2Ax^{2}+7Ax+6A+9B+3x^{2}+5x-2=8x^{2}+83-6Bx$$

Ikkala tarafdan 9B ni ayirish.

$$2Ax^{2}+7Ax+6A+3x^{2}+5x-2=8x^{2}+83-6Bx-9B$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$2Ax^{2}+7Ax+6A+5x-2=8x^{2}+83-6Bx-9B-3x^{2}$$

5x^{2} ni olish uchun 8x^{2} va -3x^{2} ni birlashtirish.

$$2Ax^{2}+7Ax+6A+5x-2=5x^{2}+83-6Bx-9B$$

Ikkala tarafdan 5x ni ayirish.

$$2Ax^{2}+7Ax+6A-2=5x^{2}+83-6Bx-9B-5x$$

2 ni ikki tarafga qo’shing.

$$2Ax^{2}+7Ax+6A=5x^{2}+83-6Bx-9B-5x+2$$

85 olish uchun 83 va 2'ni qo'shing.

$$2Ax^{2}+7Ax+6A=5x^{2}+85-6Bx-9B-5x$$

A'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x^{2}+7x+6\right)A=5x^{2}+85-6Bx-9B-5x$$

Tenglama standart shaklda.

$$\left(2x^{2}+7x+6\right)A=5x^{2}-6Bx-5x-9B+85$$

Ikki tarafini 2x^{2}+7x+6 ga bo‘ling.

$$\frac{\left(2x^{2}+7x+6\right)A}{2x^{2}+7x+6}=\frac{5x^{2}-6Bx-5x-9B+85}{2x^{2}+7x+6}$$

2x^{2}+7x+6 ga bo'lish 2x^{2}+7x+6 ga ko'paytirishni bekor qiladi.

$$A=\frac{5x^{2}-6Bx-5x-9B+85}{2x^{2}+7x+6}$$

5x^{2}+85-6Bx-9B-5x ni 2x^{2}+7x+6 ga bo'lish.

$$A=\frac{5x^{2}-6Bx-5x-9B+85}{\left(x+2\right)\left(2x+3\right)}$$

A uchun yechish

$$\left\{\begin{matrix}A=-\frac{-5x^{2}+6Bx+5x+9B-85}{\left(x+2\right)\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }x\neq -2\\A\in \mathrm{R}\text{, }&x=-2\text{ and }B=-\frac{115}{3}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

83 olish uchun 36 va 47'ni qo'shing.

$$8x^{2}+83=2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2=8x^{2}+83$$

Ikkala tarafdan 6Bx ni ayirish.

$$2Ax^{2}+7Ax+6A+9B+3x^{2}+5x-2=8x^{2}+83-6Bx$$

Ikkala tarafdan 9B ni ayirish.

$$2Ax^{2}+7Ax+6A+3x^{2}+5x-2=8x^{2}+83-6Bx-9B$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$2Ax^{2}+7Ax+6A+5x-2=8x^{2}+83-6Bx-9B-3x^{2}$$

5x^{2} ni olish uchun 8x^{2} va -3x^{2} ni birlashtirish.

$$2Ax^{2}+7Ax+6A+5x-2=5x^{2}+83-6Bx-9B$$

Ikkala tarafdan 5x ni ayirish.

$$2Ax^{2}+7Ax+6A-2=5x^{2}+83-6Bx-9B-5x$$

2 ni ikki tarafga qo’shing.

$$2Ax^{2}+7Ax+6A=5x^{2}+83-6Bx-9B-5x+2$$

85 olish uchun 83 va 2'ni qo'shing.

$$2Ax^{2}+7Ax+6A=5x^{2}+85-6Bx-9B-5x$$

A'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x^{2}+7x+6\right)A=5x^{2}+85-6Bx-9B-5x$$

Tenglama standart shaklda.

$$\left(2x^{2}+7x+6\right)A=5x^{2}-6Bx-5x-9B+85$$

Ikki tarafini 2x^{2}+7x+6 ga bo‘ling.

$$\frac{\left(2x^{2}+7x+6\right)A}{2x^{2}+7x+6}=\frac{5x^{2}-6Bx-5x-9B+85}{2x^{2}+7x+6}$$

2x^{2}+7x+6 ga bo'lish 2x^{2}+7x+6 ga ko'paytirishni bekor qiladi.

$$A=\frac{5x^{2}-6Bx-5x-9B+85}{2x^{2}+7x+6}$$

5x^{2}+85-6Bx-9B-5x ni 2x^{2}+7x+6 ga bo'lish.

$$A=\frac{5x^{2}-6Bx-5x-9B+85}{\left(x+2\right)\left(2x+3\right)}$$

B uchun yechish

$$B=-\frac{2Ax^{2}-5x^{2}+7Ax+5x+6A-85}{3\left(2x+3\right)}$$

$$x\neq -\frac{3}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

83 olish uchun 36 va 47'ni qo'shing.

$$8x^{2}+83=2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2Ax^{2}+7Ax+6A+6Bx+9B+3x^{2}+5x-2=8x^{2}+83$$

Ikkala tarafdan 2Ax^{2} ni ayirish.

$$7Ax+6A+6Bx+9B+3x^{2}+5x-2=8x^{2}+83-2Ax^{2}$$

Ikkala tarafdan 7Ax ni ayirish.

$$6A+6Bx+9B+3x^{2}+5x-2=8x^{2}+83-2Ax^{2}-7Ax$$

Ikkala tarafdan 6A ni ayirish.

$$6Bx+9B+3x^{2}+5x-2=8x^{2}+83-2Ax^{2}-7Ax-6A$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$6Bx+9B+5x-2=8x^{2}+83-2Ax^{2}-7Ax-6A-3x^{2}$$

Ikkala tarafdan 5x ni ayirish.

$$6Bx+9B-2=8x^{2}+83-2Ax^{2}-7Ax-6A-3x^{2}-5x$$

2 ni ikki tarafga qo’shing.

$$6Bx+9B=8x^{2}+83-2Ax^{2}-7Ax-6A-3x^{2}-5x+2$$

5x^{2} ni olish uchun 8x^{2} va -3x^{2} ni birlashtirish.

$$6Bx+9B=5x^{2}+83-2Ax^{2}-7Ax-6A-5x+2$$

85 olish uchun 83 va 2'ni qo'shing.

$$6Bx+9B=5x^{2}+85-2Ax^{2}-7Ax-6A-5x$$

B'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(6x+9\right)B=5x^{2}+85-2Ax^{2}-7Ax-6A-5x$$

Tenglama standart shaklda.

$$\left(6x+9\right)B=85-6A-5x-7Ax+5x^{2}-2Ax^{2}$$

Ikki tarafini 6x+9 ga bo‘ling.

$$\frac{\left(6x+9\right)B}{6x+9}=\frac{85-6A-5x-7Ax+5x^{2}-2Ax^{2}}{6x+9}$$

6x+9 ga bo'lish 6x+9 ga ko'paytirishni bekor qiladi.

$$B=\frac{85-6A-5x-7Ax+5x^{2}-2Ax^{2}}{6x+9}$$

5x^{2}+85-2Ax^{2}-7Ax-6A-5x ni 6x+9 ga bo'lish.

$$B=\frac{85-6A-5x-7Ax+5x^{2}-2Ax^{2}}{3\left(2x+3\right)}$$