sqrt{8x^2+36}-3x=0 eching

$$\sqrt { 8 x ^ { 2 } + 36 } - 3 x = 0$$

x uchun yechish

$$x=6$$

Yechim qadamlari

Tenglamaning ikkala tarafidan -3x ni ayirish.

$$\sqrt{8x^{2}+36}=3x$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{8x^{2}+36}\right)^{2}=\left(3x\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{8x^{2}+36} ga hisoblang va 8x^{2}+36 ni qiymatni oling.

$$8x^{2}+36=\left(3x\right)^{2}$$

\left(3x\right)^{2} ni kengaytirish.

$$8x^{2}+36=3^{2}x^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$8x^{2}+36=9x^{2}$$

Ikkala tarafdan 9x^{2} ni ayirish.

$$8x^{2}+36-9x^{2}=0$$

-x^{2} ni olish uchun 8x^{2} va -9x^{2} ni birlashtirish.

$$-x^{2}+36=0$$

Ikkala tarafdan 36 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x^{2}=-36$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=\frac{-36}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-36}{-1} kasrini 36 ga soddalashtirish mumkin.

$$x^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=6 x=-6$$

\sqrt{8x^{2}+36}-3x=0 tenglamasida x uchun 6 ni almashtiring.

$$\sqrt{8\times 6^{2}+36}-3\times 6=0$$

Qisqartirish. x=6 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{8x^{2}+36}-3x=0 tenglamasida x uchun -6 ni almashtiring.

$$\sqrt{8\left(-6\right)^{2}+36}-3\left(-6\right)=0$$

Qisqartirish. x=-6 qiymati bu tenglamani qoniqtirmaydi.

$$36=0$$

\sqrt{8x^{2}+36}=3x tenglamasi noyob yechimga ega.

$$x=6$$