sqrt{2x+4}-2sqrt{x-4}=0 eching

$$\sqrt { 2 x + 4 } - 2 \sqrt { x - 4 } = 0$$

x uchun yechish

$$x=10$$

Yechim qadamlari

Tenglamaning ikkala tarafidan -2\sqrt{x-4} ni ayirish.

$$\sqrt{2x+4}=2\sqrt{x-4}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

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

2 daraja ko‘rsatkichini \sqrt{2x+4} ga hisoblang va 2x+4 ni qiymatni oling.

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

\left(2\sqrt{x-4}\right)^{2} ni kengaytirish.

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

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

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

2 daraja ko‘rsatkichini \sqrt{x-4} ga hisoblang va x-4 ni qiymatni oling.

$$2x+4=4\left(x-4\right)$$

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

$$2x+4=4x-16$$

Ikkala tarafdan 4x ni ayirish.

$$2x+4-4x=-16$$

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

$$-2x+4=-16$$

Ikkala tarafdan 4 ni ayirish.

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

-20 olish uchun -16 dan 4 ni ayirish.

$$-2x=-20$$

Ikki tarafini -2 ga bo‘ling.

$$x=\frac{-20}{-2}$$

10 ni olish uchun -20 ni -2 ga bo‘ling.

$$x=10$$

\sqrt{2x+4}-2\sqrt{x-4}=0 tenglamasida x uchun 10 ni almashtiring.

$$\sqrt{2\times 10+4}-2\sqrt{10-4}=0$$

Qisqartirish. x=10 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{2x+4}=2\sqrt{x-4} tenglamasi noyob yechimga ega.

$$x=10$$