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

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

x uchun yechish

$$x=9$$

Yechim qadamlari

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

$$\sqrt{x+16}=2+\sqrt{x}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

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

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

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

$$x+16=4+4\sqrt{x}+x$$

Ikkala tarafdan 4\sqrt{x} ni ayirish.

$$x+16-4\sqrt{x}=4+x$$

Ikkala tarafdan x ni ayirish.

$$x+16-4\sqrt{x}-x=4$$

0 ni olish uchun x va -x ni birlashtirish.

$$16-4\sqrt{x}=4$$

Ikkala tarafdan 16 ni ayirish.

$$-4\sqrt{x}=4-16$$

-12 olish uchun 4 dan 16 ni ayirish.

$$-4\sqrt{x}=-12$$

Ikki tarafini -4 ga bo‘ling.

$$\sqrt{x}=\frac{-12}{-4}$$

3 ni olish uchun -12 ni -4 ga bo‘ling.

$$\sqrt{x}=3$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x=9$$

\sqrt{x+16}-\sqrt{x}=2 tenglamasida x uchun 9 ni almashtiring.

$$\sqrt{9+16}-\sqrt{9}=2$$

Qisqartirish. x=9 tenglamani qoniqtiradi.

$$2=2$$

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

$$x=9$$