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

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

x uchun yechish

$$x=7$$

Yechim qadamlari

Tenglamaning ikkala tarafidan \sqrt{x+9} ni ayirish.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(7-\sqrt{x+9}\right)^{2} kengaytirilishi uchun ishlating.

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

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

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

58 olish uchun 49 va 9'ni qo'shing.

$$x+2=58-14\sqrt{x+9}+x$$

14\sqrt{x+9} ni ikki tarafga qo’shing.

$$x+2+14\sqrt{x+9}=58+x$$

Ikkala tarafdan x ni ayirish.

$$x+2+14\sqrt{x+9}-x=58$$

0 ni olish uchun x va -x ni birlashtirish.

$$2+14\sqrt{x+9}=58$$

Ikkala tarafdan 2 ni ayirish.

$$14\sqrt{x+9}=58-2$$

56 olish uchun 58 dan 2 ni ayirish.

$$14\sqrt{x+9}=56$$

Ikki tarafini 14 ga bo‘ling.

$$\sqrt{x+9}=\frac{56}{14}$$

4 ni olish uchun 56 ni 14 ga bo‘ling.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x+9=16$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x+9-9=16-9$$

O‘zidan 9 ayirilsa 0 qoladi.

$$x=16-9$$

16 dan 9 ni ayirish.

$$x=7$$

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

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

Qisqartirish. x=7 tenglamani qoniqtiradi.

$$7=7$$

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

$$x=7$$