sqrt{x-3}=sqrt{2-x} eching

$$\sqrt { x - 3 } = \sqrt { 2 - x }$$

x uchun yechish (complex solution)

$$x = \frac{5}{2} = 2\frac{1}{2} = 2,5$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x-3}\right)^{2}=\left(\sqrt{2-x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x-3} ga hisoblang va x-3 ni qiymatni oling.

$$x-3=\left(\sqrt{2-x}\right)^{2}$$

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

$$x-3=2-x$$

x ni ikki tarafga qo’shing.

$$x-3+x=2$$

2x ni olish uchun x va x ni birlashtirish.

$$2x-3=2$$

3 ni ikki tarafga qo’shing.

$$2x=2+3$$

5 olish uchun 2 va 3'ni qo'shing.

$$2x=5$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{5}{2}$$

\sqrt{x-3}=\sqrt{2-x} tenglamasida x uchun \frac{5}{2} ni almashtiring.

$$\sqrt{\frac{5}{2}-3}=\sqrt{2-\frac{5}{2}}$$

Qisqartirish. x=\frac{5}{2} tenglamani qoniqtiradi.

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

\sqrt{x-3}=\sqrt{2-x} tenglamasi noyob yechimga ega.

$$x=\frac{5}{2}$$