(x-10)(x-1)--(x+1)(x-y)=6 eching

$$(x-10)(x-1)--(x+1)(x-y)=6$$

y uchun yechish

$$y=\frac{2\left(x^{2}-5x+2\right)}{x+1}$$

$$x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x-10 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-11x+10-\left(-\left(x+1\right)\right)\left(x-y\right)=6$$

x+1 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-11x+10-\left(-x-1\right)\left(x-y\right)=6$$

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

$$x^{2}-11x+10-\left(-x^{2}+xy-x+y\right)=6$$

-x^{2}+xy-x+y teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-11x+10+x^{2}-xy+x-y=6$$

2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.

$$2x^{2}-11x+10-xy+x-y=6$$

-10x ni olish uchun -11x va x ni birlashtirish.

$$2x^{2}-10x+10-xy-y=6$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$-10x+10-xy-y=6-2x^{2}$$

10x ni ikki tarafga qo’shing.

$$10-xy-y=6-2x^{2}+10x$$

Ikkala tarafdan 10 ni ayirish.

$$-xy-y=6-2x^{2}+10x-10$$

-4 olish uchun 6 dan 10 ni ayirish.

$$-xy-y=-4-2x^{2}+10x$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x-1\right)y=-4-2x^{2}+10x$$

Tenglama standart shaklda.

$$\left(-x-1\right)y=-2x^{2}+10x-4$$

Ikki tarafini -x-1 ga bo‘ling.

$$\frac{\left(-x-1\right)y}{-x-1}=\frac{-2x^{2}+10x-4}{-x-1}$$

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

$$y=\frac{-2x^{2}+10x-4}{-x-1}$$

-4-2x^{2}+10x ni -x-1 ga bo'lish.

$$y=-\frac{2\left(-x^{2}+5x-2\right)}{x+1}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}$$

x uchun yechish

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}\text{, }y\geq 8\sqrt{2}-14\text{ or }y\leq -8\sqrt{2}-14$$