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

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

x uchun yechish

$$x=-2$$

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

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

$$x^{2}+4x+4=4-x^{2}$$

Ikkala tarafdan 4 ni ayirish.

$$x^{2}+4x+4-4=-x^{2}$$

0 olish uchun 4 dan 4 ni ayirish.

$$x^{2}+4x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$x^{2}+4x+x^{2}=0$$

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

$$2x^{2}+4x=0$$

x omili.

$$x\left(2x+4\right)=0$$

Tenglamani yechish uchun x=0 va 2x+4=0 ni yeching.

$$x=0 x=-2$$

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

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

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$2=2$$

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

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

Qisqartirish. x=-2 tenglamani qoniqtiradi.

$$0=0$$

x+2=\sqrt{4-x^{2}} boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=-2$$