sqrt{x+9}+sqrt{x+2}=7 eching

$$\sqrt { x + 9 } + \sqrt { x + 2 } = 7$$

x uchun yechish

$$x=7$$

Yechim qadamlari

Tenglamaning ikkala tarafidan \sqrt{x+2} ni ayirish.

$$\sqrt{x+9}=7-\sqrt{x+2}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x+9}\right)^{2}=\left(7-\sqrt{x+2}\right)^{2}$$

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

$$x+9=\left(7-\sqrt{x+2}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(7-\sqrt{x+2}\right)^{2} kengaytirilishi uchun ishlating.

$$x+9=49-14\sqrt{x+2}+\left(\sqrt{x+2}\right)^{2}$$

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

$$x+9=49-14\sqrt{x+2}+x+2$$

51 olish uchun 49 va 2'ni qo'shing.

$$x+9=51-14\sqrt{x+2}+x$$

14\sqrt{x+2} ni ikki tarafga qo’shing.

$$x+9+14\sqrt{x+2}=51+x$$

Ikkala tarafdan x ni ayirish.

$$x+9+14\sqrt{x+2}-x=51$$

0 ni olish uchun x va -x ni birlashtirish.

$$9+14\sqrt{x+2}=51$$

Ikkala tarafdan 9 ni ayirish.

$$14\sqrt{x+2}=51-9$$

42 olish uchun 51 dan 9 ni ayirish.

$$14\sqrt{x+2}=42$$

Ikki tarafini 14 ga bo‘ling.

$$\sqrt{x+2}=\frac{42}{14}$$

3 ni olish uchun 42 ni 14 ga bo‘ling.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x+2=9$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x+2-2=9-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x=9-2$$

9 dan 2 ni ayirish.

$$x=7$$

\sqrt{x+9}+\sqrt{x+2}=7 tenglamasida x uchun 7 ni almashtiring.

$$\sqrt{7+9}+\sqrt{7+2}=7$$

Qisqartirish. x=7 tenglamani qoniqtiradi.

$$7=7$$

\sqrt{x+9}=-\sqrt{x+2}+7 tenglamasi noyob yechimga ega.

$$x=7$$