sqrt{3x+4}=sqrt{2x+5} eching

$$\sqrt{ 3x+4 } = \sqrt{ 2x+5 }$$

x uchun yechish

$$x=1$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{3x+4}\right)^{2}=\left(\sqrt{2x+5}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{3x+4} ga hisoblang va 3x+4 ni qiymatni oling.

$$3x+4=\left(\sqrt{2x+5}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{2x+5} ga hisoblang va 2x+5 ni qiymatni oling.

$$3x+4=2x+5$$

Ikkala tarafdan 2x ni ayirish.

$$3x+4-2x=5$$

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

$$x+4=5$$

Ikkala tarafdan 4 ni ayirish.

$$x=5-4$$

1 olish uchun 5 dan 4 ni ayirish.

$$x=1$$

\sqrt{3x+4}=\sqrt{2x+5} tenglamasida x uchun 1 ni almashtiring.

$$\sqrt{3\times 1+4}=\sqrt{2\times 1+5}$$

Qisqartirish. x=1 tenglamani qoniqtiradi.

$$7^{\frac{1}{2}}=7^{\frac{1}{2}}$$

\sqrt{3x+4}=\sqrt{2x+5} tenglamasi noyob yechimga ega.

$$x=1$$