x=sqrt{4-x^2} eching

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

x uchun yechish

$$x=\sqrt{2}\approx 1,414213562$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

x^{2} ni ikki tarafga qo’shing.

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

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

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

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{4}{2}$$

2 ni olish uchun 4 ni 2 ga bo‘ling.

$$x^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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

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

Qisqartirish. x=\sqrt{2} tenglamani qoniqtiradi.

$$2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

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

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

Qisqartirish. x=-\sqrt{2} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$-2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

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

$$x=\sqrt{2}$$