sqrt{x+3}=sqrt{1-x} eching

$$\sqrt { x + 3 } = \sqrt { 1 - x }$$

x uchun yechish

$$x=-1$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x+3}\right)^{2}=\left(\sqrt{1-x}\right)^{2}$$

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

$$x+3=\left(\sqrt{1-x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{1-x} ga hisoblang va 1-x ni qiymatni oling.

$$x+3=1-x$$

x ni ikki tarafga qo’shing.

$$x+3+x=1$$

2x ni olish uchun x va x ni birlashtirish.

$$2x+3=1$$

Ikkala tarafdan 3 ni ayirish.

$$2x=1-3$$

-2 olish uchun 1 dan 3 ni ayirish.

$$2x=-2$$

Ikki tarafini 2 ga bo‘ling.

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

-1 ni olish uchun -2 ni 2 ga bo‘ling.

$$x=-1$$

\sqrt{x+3}=\sqrt{1-x} tenglamasida x uchun -1 ni almashtiring.

$$\sqrt{-1+3}=\sqrt{1-\left(-1\right)}$$

Qisqartirish. x=-1 tenglamani qoniqtiradi.

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

\sqrt{x+3}=\sqrt{1-x} tenglamasi noyob yechimga ega.

$$x=-1$$