left(2-mright)x^2-left(3m+1right)x+4=0 eching

$$\left( 2-m \right) { x }^{ 2 } - \left( 3m+1 \right) x+4 = 0$$

m uchun yechish

$$m=\frac{2x^{2}-x+4}{x\left(x+3\right)}$$

$$x\neq -3\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x^{2}-mx^{2}-\left(3m+1\right)x+4=0$$

3m+1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-mx^{2}-\left(3mx+x\right)+4=0$$

3mx+x teskarisini topish uchun har birining teskarisini toping.

$$2x^{2}-mx^{2}-3mx-x+4=0$$

Ikkala tarafdan 2x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-mx^{2}-3mx-x+4=-2x^{2}$$

x ni ikki tarafga qo’shing.

$$-mx^{2}-3mx+4=-2x^{2}+x$$

Ikkala tarafdan 4 ni ayirish.

$$-mx^{2}-3mx=-2x^{2}+x-4$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini -x^{2}-3x ga bo‘ling.

$$\frac{\left(-x^{2}-3x\right)m}{-x^{2}-3x}=\frac{-2x^{2}+x-4}{-x^{2}-3x}$$

-x^{2}-3x ga bo'lish -x^{2}-3x ga ko'paytirishni bekor qiladi.

$$m=\frac{-2x^{2}+x-4}{-x^{2}-3x}$$

-2x^{2}+x-4 ni -x^{2}-3x ga bo'lish.

$$m=\frac{-2x^{2}+x-4}{-x\left(x+3\right)}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(m-1\right)\left(9m+31\right)}+3m+1}{2\left(2-m\right)}\text{; }x=\frac{-\sqrt{\left(m-1\right)\left(9m+31\right)}+3m+1}{2\left(2-m\right)}\text{, }&m\neq 2\\x=\frac{4}{7}\text{, }&m=2\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(m-1\right)\left(9m+31\right)}+3m+1}{2\left(2-m\right)}\text{; }x=\frac{-\sqrt{\left(m-1\right)\left(9m+31\right)}+3m+1}{2\left(2-m\right)}\text{, }&\left(m\neq 2\text{ and }m\geq 1\right)\text{ or }m\leq -\frac{31}{9}\\x=\frac{4}{7}\text{, }&m=2\end{matrix}\right,$$