12/3a^2+2=3 eching

$$\frac { 12 } { 3 a ^ { 2 } + 2 } = 3$$

a uchun yechish

$$a=\frac{\sqrt{6}}{3}\approx 0,816496581$$

$$a=-\frac{\sqrt{6}}{3}\approx -0,816496581$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 3a^{2}+2 ga ko'paytirish.

$$12=3\left(3a^{2}+2\right)$$

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

$$12=9a^{2}+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9a^{2}+6=12$$

Ikkala tarafdan 6 ni ayirish.

$$9a^{2}=12-6$$

6 olish uchun 12 dan 6 ni ayirish.

$$9a^{2}=6$$

Ikki tarafini 9 ga bo‘ling.

$$a^{2}=\frac{6}{9}$$

\frac{6}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a^{2}=\frac{2}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$a=\frac{\sqrt{6}}{3} a=-\frac{\sqrt{6}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3a^{2}+2 ga ko'paytirish.

$$12=3\left(3a^{2}+2\right)$$

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

$$12=9a^{2}+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9a^{2}+6=12$$

Ikkala tarafdan 12 ni ayirish.

$$9a^{2}+6-12=0$$

-6 olish uchun 6 dan 12 ni ayirish.

$$9a^{2}-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 0 ni b va -6 ni c bilan almashtiring.

$$a=\frac{0±\sqrt{0^{2}-4\times 9\left(-6\right)}}{2\times 9}$$

0 kvadratini chiqarish.

$$a=\frac{0±\sqrt{-4\times 9\left(-6\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{-36\left(-6\right)}}{2\times 9}$$

-36 ni -6 marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{216}}{2\times 9}$$

216 ning kvadrat ildizini chiqarish.

$$a=\frac{0±6\sqrt{6}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$a=\frac{0±6\sqrt{6}}{18}$$

a=\frac{0±6\sqrt{6}}{18} tenglamasini yeching, bunda ± musbat.

$$a=\frac{\sqrt{6}}{3}$$

a=\frac{0±6\sqrt{6}}{18} tenglamasini yeching, bunda ± manfiy.

$$a=-\frac{\sqrt{6}}{3}$$

Tenglama yechildi.

$$a=\frac{\sqrt{6}}{3} a=-\frac{\sqrt{6}}{3}$$