frac{sqrt{3}}{4}*(2-frac{2sqrt{3}}{3})^2*6 eching

$$\frac { \sqrt { 3 } } { 4 } \times ( 2 - \frac { 2 \sqrt { 3 } } { 3 } ) ^ { 2 } \times 6$$

Baholash

$$8\sqrt{3}-12\approx 1,856406461$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{3}{3} marotabaga ko'paytirish.

$$6\times \frac{\sqrt{3}}{4}\left(\frac{2\times 3}{3}-\frac{2\sqrt{3}}{3}\right)^{2}$$

\frac{2\times 3}{3} va \frac{2\sqrt{3}}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$6\times \frac{\sqrt{3}}{4}\times \left(\frac{2\times 3-2\sqrt{3}}{3}\right)^{2}$$

2\times 3-2\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$6\times \frac{\sqrt{3}}{4}\times \left(\frac{6-2\sqrt{3}}{3}\right)^{2}$$

\frac{6-2\sqrt{3}}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$6\times \frac{\sqrt{3}}{4}\times \frac{\left(6-2\sqrt{3}\right)^{2}}{3^{2}}$$

6\times \frac{\sqrt{3}}{4} ni yagona kasrga aylantiring.

$$\frac{6\sqrt{3}}{4}\times \frac{\left(6-2\sqrt{3}\right)^{2}}{3^{2}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{6\sqrt{3}}{4} ni \frac{\left(6-2\sqrt{3}\right)^{2}}{3^{2}} ga ko‘paytiring.

$$\frac{6\sqrt{3}\left(6-2\sqrt{3}\right)^{2}}{4\times 3^{2}}$$

Surat va maxrajdagi ikkala 2\times 3 ni qisqartiring.

$$\frac{\sqrt{3}\left(-2\sqrt{3}+6\right)^{2}}{2\times 3}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-2\sqrt{3}+6\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{\sqrt{3}\left(4\left(\sqrt{3}\right)^{2}-24\sqrt{3}+36\right)}{2\times 3}$$

\sqrt{3} kvadrati – 3.

$$\frac{\sqrt{3}\left(4\times 3-24\sqrt{3}+36\right)}{2\times 3}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{\sqrt{3}\left(12-24\sqrt{3}+36\right)}{2\times 3}$$

48 olish uchun 12 va 36'ni qo'shing.

$$\frac{\sqrt{3}\left(48-24\sqrt{3}\right)}{2\times 3}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{\sqrt{3}\left(48-24\sqrt{3}\right)}{6}$$

\sqrt{3} ga 48-24\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{48\sqrt{3}-24\left(\sqrt{3}\right)^{2}}{6}$$

\sqrt{3} kvadrati – 3.

$$\frac{48\sqrt{3}-24\times 3}{6}$$

-72 hosil qilish uchun -24 va 3 ni ko'paytirish.

$$\frac{48\sqrt{3}-72}{6}$$