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

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

x uchun yechish

$$x=2$$

Yechim qadamlari

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

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2+\sqrt{x-2}\right)^{2} kengaytirilishi uchun ishlating.

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

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

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

2 olish uchun 4 dan 2 ni ayirish.

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

Ikkala tarafdan 4\sqrt{x-2} ni ayirish.

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

Ikkala tarafdan x ni ayirish.

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

0 ni olish uchun x va -x ni birlashtirish.

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

Ikkala tarafdan 2 ni ayirish.

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

0 olish uchun 2 dan 2 ni ayirish.

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

Ikki tarafini -4 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x-2=0$$

2 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -2 ayirilsa 0 qoladi.

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

0 dan -2 ni ayirish.

$$x=2$$

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

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

Qisqartirish. x=2 tenglamani qoniqtiradi.

$$2=2$$

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

$$x=2$$