sqrt{x}-2=sqrt{x-56} eching

$$\sqrt { x } - 2 = \sqrt { x - 56 }$$

x uchun yechish

$$x=225$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x}-2\right)^{2}=\left(\sqrt{x-56}\right)^{2}$$

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

$$\left(\sqrt{x}\right)^{2}-4\sqrt{x}+4=\left(\sqrt{x-56}\right)^{2}$$

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

$$x-4\sqrt{x}+4=\left(\sqrt{x-56}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x-56} ga hisoblang va x-56 ni qiymatni oling.

$$x-4\sqrt{x}+4=x-56$$

Ikkala tarafdan x ni ayirish.

$$x-4\sqrt{x}+4-x=-56$$

0 ni olish uchun x va -x ni birlashtirish.

$$-4\sqrt{x}+4=-56$$

Ikkala tarafdan 4 ni ayirish.

$$-4\sqrt{x}=-56-4$$

-60 olish uchun -56 dan 4 ni ayirish.

$$-4\sqrt{x}=-60$$

Ikki tarafini -4 ga bo‘ling.

$$\sqrt{x}=\frac{-60}{-4}$$

15 ni olish uchun -60 ni -4 ga bo‘ling.

$$\sqrt{x}=15$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x=225$$

\sqrt{x}-2=\sqrt{x-56} tenglamasida x uchun 225 ni almashtiring.

$$\sqrt{225}-2=\sqrt{225-56}$$

Qisqartirish. x=225 tenglamani qoniqtiradi.

$$13=13$$

\sqrt{x}-2=\sqrt{x-56} tenglamasi noyob yechimga ega.

$$x=225$$