P(x)+P(x-1)=2x^2-4x+2 eching

$$P ( x ) + P ( x - 1 ) = 2 x ^ { 2 } - 4 x + 2$$

P uchun yechish

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

$$x\neq \frac{1}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$Px+Px-P=2x^{2}-4x+2$$

2Px ni olish uchun Px va Px ni birlashtirish.

$$2Px-P=2x^{2}-4x+2$$

P'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini 2x-1 ga bo‘ling.

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

2x-1 ga bo'lish 2x-1 ga ko'paytirishni bekor qiladi.

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

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{P\left(P+2\right)}+P+2}{2}$$

$$x=\frac{\sqrt{P\left(P+2\right)}+P+2}{2}$$

x uchun yechish

$$x=\frac{-\sqrt{P\left(P+2\right)}+P+2}{2}$$

$$x=\frac{\sqrt{P\left(P+2\right)}+P+2}{2}\text{, }P\leq -2\text{ or }P\geq 0$$