sqrt{9x-28}=sqrt{5x} eching

$$\sqrt { 9 x - 28 } = \sqrt { 5 x }$$

x uchun yechish

$$x=7$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{9x-28}\right)^{2}=\left(\sqrt{5x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{9x-28} ga hisoblang va 9x-28 ni qiymatni oling.

$$9x-28=\left(\sqrt{5x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{5x} ga hisoblang va 5x ni qiymatni oling.

$$9x-28=5x$$

Ikkala tarafdan 5x ni ayirish.

$$9x-28-5x=0$$

4x ni olish uchun 9x va -5x ni birlashtirish.

$$4x-28=0$$

28 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$4x=28$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{28}{4}$$

7 ni olish uchun 28 ni 4 ga bo‘ling.

$$x=7$$

\sqrt{9x-28}=\sqrt{5x} tenglamasida x uchun 7 ni almashtiring.

$$\sqrt{9\times 7-28}=\sqrt{5\times 7}$$

Qisqartirish. x=7 tenglamani qoniqtiradi.

$$35^{\frac{1}{2}}=35^{\frac{1}{2}}$$

\sqrt{9x-28}=\sqrt{5x} tenglamasi noyob yechimga ega.

$$x=7$$