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

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

m uchun yechish (complex solution)

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

$$x\neq -i\text{ and }x\neq i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

-2 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-2x+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x^{2} ni ikki tarafga qo’shing.

$$mx^{2}+2x+m=3+2x^{2}$$

Ikkala tarafdan 2x ni ayirish.

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

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x^{2}+1 ga bo‘ling.

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

x^{2}+1 ga bo'lish x^{2}+1 ga ko'paytirishni bekor qiladi.

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

m uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

-2 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-2x+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x^{2} ni ikki tarafga qo’shing.

$$mx^{2}+2x+m=3+2x^{2}$$

Ikkala tarafdan 2x ni ayirish.

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

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x^{2}+1 ga bo‘ling.

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

x^{2}+1 ga bo'lish x^{2}+1 ga ko'paytirishni bekor qiladi.

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

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\text{ and }m\geq \frac{5-\sqrt{5}}{2}\text{ and }m\leq \frac{\sqrt{5}+5}{2}\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right,$$