sqrt{z}-7=sqrt{z-105} eching

$$\sqrt { z } - 7 = \sqrt { z - 105 }$$

z uchun yechish

$$z=121$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{z}-7\right)^{2}=\left(\sqrt{z-105}\right)^{2}$$

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

$$\left(\sqrt{z}\right)^{2}-14\sqrt{z}+49=\left(\sqrt{z-105}\right)^{2}$$

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

$$z-14\sqrt{z}+49=\left(\sqrt{z-105}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{z-105} ga hisoblang va z-105 ni qiymatni oling.

$$z-14\sqrt{z}+49=z-105$$

Ikkala tarafdan z ni ayirish.

$$z-14\sqrt{z}+49-z=-105$$

0 ni olish uchun z va -z ni birlashtirish.

$$-14\sqrt{z}+49=-105$$

Ikkala tarafdan 49 ni ayirish.

$$-14\sqrt{z}=-105-49$$

-154 olish uchun -105 dan 49 ni ayirish.

$$-14\sqrt{z}=-154$$

Ikki tarafini -14 ga bo‘ling.

$$\sqrt{z}=\frac{-154}{-14}$$

11 ni olish uchun -154 ni -14 ga bo‘ling.

$$\sqrt{z}=11$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$z=121$$

\sqrt{z}-7=\sqrt{z-105} tenglamasida z uchun 121 ni almashtiring.

$$\sqrt{121}-7=\sqrt{121-105}$$

Qisqartirish. z=121 tenglamani qoniqtiradi.

$$4=4$$

\sqrt{z}-7=\sqrt{z-105} tenglamasi noyob yechimga ega.

$$z=121$$