sqrt{-2x-4}=sqrt{-9+3x} eching

$$\sqrt { - 2 x - 4 } = \sqrt { - 9 + 3 x }$$

x uchun yechish (complex solution)

$$x=1$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{-2x-4}\right)^{2}=\left(\sqrt{-9+3x}\right)^{2}$$

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

$$-2x-4=\left(\sqrt{-9+3x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{-9+3x} ga hisoblang va -9+3x ni qiymatni oling.

$$-2x-4=-9+3x$$

Ikkala tarafdan 3x ni ayirish.

$$-2x-4-3x=-9$$

-5x ni olish uchun -2x va -3x ni birlashtirish.

$$-5x-4=-9$$

4 ni ikki tarafga qo’shing.

$$-5x=-9+4$$

-5 olish uchun -9 va 4'ni qo'shing.

$$-5x=-5$$

Ikki tarafini -5 ga bo‘ling.

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

1 ni olish uchun -5 ni -5 ga bo‘ling.

$$x=1$$

\sqrt{-2x-4}=\sqrt{-9+3x} tenglamasida x uchun 1 ni almashtiring.

$$\sqrt{-2-4}=\sqrt{-9+3\times 1}$$

Qisqartirish. x=1 tenglamani qoniqtiradi.

$$i\times 6^{\frac{1}{2}}=i\times 6^{\frac{1}{2}}$$

\sqrt{-2x-4}=\sqrt{3x-9} tenglamasi noyob yechimga ega.

$$x=1$$