sqrt{4x-8}=sqrt{x+7} eching

$$\sqrt { 4 x - 8 } = \sqrt { x + 7 }$$

x uchun yechish

$$x=5$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{4x-8}\right)^{2}=\left(\sqrt{x+7}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{4x-8} ga hisoblang va 4x-8 ni qiymatni oling.

$$4x-8=\left(\sqrt{x+7}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x+7} ga hisoblang va x+7 ni qiymatni oling.

$$4x-8=x+7$$

Ikkala tarafdan x ni ayirish.

$$4x-8-x=7$$

3x ni olish uchun 4x va -x ni birlashtirish.

$$3x-8=7$$

8 ni ikki tarafga qo’shing.

$$3x=7+8$$

15 olish uchun 7 va 8'ni qo'shing.

$$3x=15$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{15}{3}$$

5 ni olish uchun 15 ni 3 ga bo‘ling.

$$x=5$$

\sqrt{4x-8}=\sqrt{x+7} tenglamasida x uchun 5 ni almashtiring.

$$\sqrt{4\times 5-8}=\sqrt{5+7}$$

Qisqartirish. x=5 tenglamani qoniqtiradi.

$$2\times 3^{\frac{1}{2}}=2\times 3^{\frac{1}{2}}$$

\sqrt{4x-8}=\sqrt{x+7} tenglamasi noyob yechimga ega.

$$x=5$$