sqrt{x+4}=1+sqrt{x-9} eching

$$\sqrt { x + 4 } = 1 + \sqrt { x - 9 }$$

x uchun yechish

$$x=45$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x+4}\right)^{2}=\left(1+\sqrt{x-9}\right)^{2}$$

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

$$x+4=\left(1+\sqrt{x-9}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+\sqrt{x-9}\right)^{2} kengaytirilishi uchun ishlating.

$$x+4=1+2\sqrt{x-9}+\left(\sqrt{x-9}\right)^{2}$$

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

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

-8 olish uchun 1 dan 9 ni ayirish.

$$x+4=-8+2\sqrt{x-9}+x$$

Ikkala tarafdan 2\sqrt{x-9} ni ayirish.

$$x+4-2\sqrt{x-9}=-8+x$$

Ikkala tarafdan x ni ayirish.

$$x+4-2\sqrt{x-9}-x=-8$$

0 ni olish uchun x va -x ni birlashtirish.

$$4-2\sqrt{x-9}=-8$$

Ikkala tarafdan 4 ni ayirish.

$$-2\sqrt{x-9}=-8-4$$

-12 olish uchun -8 dan 4 ni ayirish.

$$-2\sqrt{x-9}=-12$$

Ikki tarafini -2 ga bo‘ling.

$$\sqrt{x-9}=\frac{-12}{-2}$$

6 ni olish uchun -12 ni -2 ga bo‘ling.

$$\sqrt{x-9}=6$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x-9=36$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x-9-\left(-9\right)=36-\left(-9\right)$$

O‘zidan -9 ayirilsa 0 qoladi.

$$x=36-\left(-9\right)$$

36 dan -9 ni ayirish.

$$x=45$$

\sqrt{x+4}=1+\sqrt{x-9} tenglamasida x uchun 45 ni almashtiring.

$$\sqrt{45+4}=1+\sqrt{45-9}$$

Qisqartirish. x=45 tenglamani qoniqtiradi.

$$7=7$$

\sqrt{x+4}=\sqrt{x-9}+1 tenglamasi noyob yechimga ega.

$$x=45$$