x^2-2(m-1)x+2m+1=0 eching

$$x ^ { 2 } - 2 ( m - 1 ) x + 2 m + 1 = 0$$

m uchun yechish

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

$$x\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

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

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

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

$$x^{2}-2mx+2x+2m=-1$$

Ikkala tarafdan x^{2} ni ayirish.

$$-2mx+2x+2m=-1-x^{2}$$

Ikkala tarafdan 2x ni ayirish.

$$-2mx+2m=-1-x^{2}-2x$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini -2x+2 ga bo‘ling.

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

-2x+2 ga bo'lish -2x+2 ga ko'paytirishni bekor qiladi.

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

-\left(x+1\right)^{2} ni -2x+2 ga bo'lish.

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

x uchun yechish (complex solution)

$$x=\sqrt{m\left(m-4\right)}+m-1$$

$$x=-\sqrt{m\left(m-4\right)}+m-1$$

x uchun yechish

$$x=\sqrt{m\left(m-4\right)}+m-1$$

$$x=-\sqrt{m\left(m-4\right)}+m-1\text{, }m\geq 4\text{ or }m\leq 0$$