sqrt{2u+3}=sqrt{-2u-1} eching

$$\sqrt { 2 u + 3 } = \sqrt { - 2 u - 1 }$$

u uchun yechish

$$u=-1$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

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

$$2u+3=-2u-1$$

2u ni ikki tarafga qo’shing.

$$2u+3+2u=-1$$

4u ni olish uchun 2u va 2u ni birlashtirish.

$$4u+3=-1$$

Ikkala tarafdan 3 ni ayirish.

$$4u=-1-3$$

-4 olish uchun -1 dan 3 ni ayirish.

$$4u=-4$$

Ikki tarafini 4 ga bo‘ling.

$$u=\frac{-4}{4}$$

-1 ni olish uchun -4 ni 4 ga bo‘ling.

$$u=-1$$

\sqrt{2u+3}=\sqrt{-2u-1} tenglamasida u uchun -1 ni almashtiring.

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

Qisqartirish. u=-1 tenglamani qoniqtiradi.

$$1=1$$

\sqrt{2u+3}=\sqrt{-2u-1} tenglamasi noyob yechimga ega.

$$u=-1$$