sqrt{x-3}+sqrt{x}=3 eching

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

x uchun yechish

$$x=4$$

Yechim qadamlari

Tenglamaning ikkala tarafidan \sqrt{x} ni ayirish.

$$\sqrt{x-3}=3-\sqrt{x}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

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

2 daraja ko‘rsatkichini \sqrt{x-3} ga hisoblang va x-3 ni qiymatni oling.

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

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

$$x-3=9-6\sqrt{x}+\left(\sqrt{x}\right)^{2}$$

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

$$x-3=9-6\sqrt{x}+x$$

6\sqrt{x} ni ikki tarafga qo’shing.

$$x-3+6\sqrt{x}=9+x$$

Ikkala tarafdan x ni ayirish.

$$x-3+6\sqrt{x}-x=9$$

0 ni olish uchun x va -x ni birlashtirish.

$$-3+6\sqrt{x}=9$$

3 ni ikki tarafga qo’shing.

$$6\sqrt{x}=9+3$$

12 olish uchun 9 va 3'ni qo'shing.

$$6\sqrt{x}=12$$

Ikki tarafini 6 ga bo‘ling.

$$\sqrt{x}=\frac{12}{6}$$

2 ni olish uchun 12 ni 6 ga bo‘ling.

$$\sqrt{x}=2$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x=4$$

\sqrt{x-3}+\sqrt{x}=3 tenglamasida x uchun 4 ni almashtiring.

$$\sqrt{4-3}+\sqrt{4}=3$$

Qisqartirish. x=4 tenglamani qoniqtiradi.

$$3=3$$

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

$$x=4$$