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

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

m uchun yechish

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

$$x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x^{2}+mx+3x+m-1=0$$

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

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

Ikkala tarafdan 3x ni ayirish.

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

1 ni ikki tarafga qo’shing.

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

m'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x+1 ga bo‘ling.

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

x+1 ga bo'lish x+1 ga ko'paytirishni bekor qiladi.

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

x uchun yechish

$$x=\frac{\sqrt{m^{2}-2m+17}-m-3}{4}$$

$$x=\frac{-\sqrt{m^{2}-2m+17}-m-3}{4}$$