1/2=frac{sqrt{a^2-3}}{a} eching

$$\frac { 1 } { 2 } = \frac { \sqrt { a ^ { 2 } - 3 } } { a }$$

a uchun yechish

$$a=2$$

Yechim qadamlari

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2a ga, 2,a ning eng kichik karralisiga ko‘paytiring.

$$a=2\sqrt{a^{2}-3}$$

Ikkala tarafdan 2\sqrt{a^{2}-3} ni ayirish.

$$a-2\sqrt{a^{2}-3}=0$$

Tenglamaning ikkala tarafidan a ni ayirish.

$$-2\sqrt{a^{2}-3}=-a$$

Tenglamaning ikkala taraf kvadratini chiqarish.

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

\left(-2\sqrt{a^{2}-3}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

$$4\left(\sqrt{a^{2}-3}\right)^{2}=\left(-a\right)^{2}$$

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

$$4\left(a^{2}-3\right)=\left(-a\right)^{2}$$

4 ga a^{2}-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4a^{2}-12=\left(-a\right)^{2}$$

\left(-a\right)^{2} ni kengaytirish.

$$4a^{2}-12=\left(-1\right)^{2}a^{2}$$

2 daraja ko‘rsatkichini -1 ga hisoblang va 1 ni qiymatni oling.

$$4a^{2}-12=1a^{2}$$

Ikkala tarafdan 1a^{2} ni ayirish.

$$4a^{2}-12-a^{2}=0$$

3a^{2} ni olish uchun 4a^{2} va -a^{2} ni birlashtirish.

$$3a^{2}-12=0$$

Ikki tarafini 3 ga bo‘ling.

$$a^{2}-4=0$$

Hisoblang: a^{2}-4. a^{2}-4 ni a^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-2\right)\left(a+2\right)=0$$

Tenglamani yechish uchun a-2=0 va a+2=0 ni yeching.

$$a=2 a=-2$$

\frac{1}{2}=\frac{\sqrt{a^{2}-3}}{a} tenglamasida a uchun 2 ni almashtiring.

$$\frac{1}{2}=\frac{\sqrt{2^{2}-3}}{2}$$

Qisqartirish. a=2 tenglamani qoniqtiradi.

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

\frac{1}{2}=\frac{\sqrt{a^{2}-3}}{a} tenglamasida a uchun -2 ni almashtiring.

$$\frac{1}{2}=\frac{\sqrt{\left(-2\right)^{2}-3}}{-2}$$

Qisqartirish. a=-2 qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$\frac{1}{2}=-\frac{1}{2}$$

-2\sqrt{a^{2}-3}=-a tenglamasi noyob yechimga ega.

$$a=2$$