sqrt{16-2x}=2sqrt{x-8} eching

$$\sqrt { 16 - 2 x } = 2 \sqrt { x - 8 }$$

x uchun yechish

$$x=8$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{16-2x}\right)^{2}=\left(2\sqrt{x-8}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{16-2x} ga hisoblang va 16-2x ni qiymatni oling.

$$16-2x=\left(2\sqrt{x-8}\right)^{2}$$

\left(2\sqrt{x-8}\right)^{2} ni kengaytirish.

$$16-2x=2^{2}\left(\sqrt{x-8}\right)^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$16-2x=4\left(\sqrt{x-8}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x-8} ga hisoblang va x-8 ni qiymatni oling.

$$16-2x=4\left(x-8\right)$$

4 ga x-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16-2x=4x-32$$

Ikkala tarafdan 4x ni ayirish.

$$16-2x-4x=-32$$

-6x ni olish uchun -2x va -4x ni birlashtirish.

$$16-6x=-32$$

Ikkala tarafdan 16 ni ayirish.

$$-6x=-32-16$$

-48 olish uchun -32 dan 16 ni ayirish.

$$-6x=-48$$

Ikki tarafini -6 ga bo‘ling.

$$x=\frac{-48}{-6}$$

8 ni olish uchun -48 ni -6 ga bo‘ling.

$$x=8$$

\sqrt{16-2x}=2\sqrt{x-8} tenglamasida x uchun 8 ni almashtiring.

$$\sqrt{16-2\times 8}=2\sqrt{8-8}$$

Qisqartirish. x=8 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{16-2x}=2\sqrt{x-8} tenglamasi noyob yechimga ega.

$$x=8$$