sqrt{x+2}+sqrt{x-1}=sqrt{9} eching

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

x uchun yechish

$$x=2$$

Yechim qadamlari

Tenglamaning ikkala tarafidan \sqrt{x-1} ni ayirish.

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

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3-\sqrt{x-1}\right)^{2} kengaytirilishi uchun ishlating.

$$x+2=9-6\sqrt{x-1}+\left(\sqrt{x-1}\right)^{2}$$

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

$$x+2=9-6\sqrt{x-1}+x-1$$

8 olish uchun 9 dan 1 ni ayirish.

$$x+2=8-6\sqrt{x-1}+x$$

6\sqrt{x-1} ni ikki tarafga qo’shing.

$$x+2+6\sqrt{x-1}=8+x$$

Ikkala tarafdan x ni ayirish.

$$x+2+6\sqrt{x-1}-x=8$$

0 ni olish uchun x va -x ni birlashtirish.

$$2+6\sqrt{x-1}=8$$

Ikkala tarafdan 2 ni ayirish.

$$6\sqrt{x-1}=8-2$$

6 olish uchun 8 dan 2 ni ayirish.

$$6\sqrt{x-1}=6$$

Ikki tarafini 6 ga bo‘ling.

$$\sqrt{x-1}=\frac{6}{6}$$

1 ni olish uchun 6 ni 6 ga bo‘ling.

$$\sqrt{x-1}=1$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x-1=1$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x-1-\left(-1\right)=1-\left(-1\right)$$

O‘zidan -1 ayirilsa 0 qoladi.

$$x=1-\left(-1\right)$$

1 dan -1 ni ayirish.

$$x=2$$

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

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

Qisqartirish. x=2 tenglamani qoniqtiradi.

$$3=3$$

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

$$x=2$$