{left(1+sqrt{3}right)}^2+{left(frac{sqrt{3}}{3}+1right)}^2= eching

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

Baholash

$$\frac{8\left(\sqrt{3}+2\right)}{3}\approx 9,952135487$$

Qisqa yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{3} kvadrati – 3.

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

4 olish uchun 1 va 3'ni qo'shing.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{3}{3} marotabaga ko'paytirish.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+\frac{3}{3}\right)^{2}$$

\frac{\sqrt{3}}{3} va \frac{3}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}+3}{3}\right)^{2}$$

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

$$4+2\sqrt{3}+\frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4+2\sqrt{3} ni \frac{3^{2}}{3^{2}} marotabaga ko'paytirish.

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

\frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} va \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9 hisob-kitobini qiling.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

3^{2} ni kengaytirish.

$$\frac{48+24\sqrt{3}}{9}$$

Kengaytirish

$$\frac{8 \sqrt{3} + 16}{3} = 9,95213548685034$$

Qisqa yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{3} kvadrati – 3.

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

4 olish uchun 1 va 3'ni qo'shing.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{3}{3} marotabaga ko'paytirish.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+\frac{3}{3}\right)^{2}$$

\frac{\sqrt{3}}{3} va \frac{3}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}+3}{3}\right)^{2}$$

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

$$4+2\sqrt{3}+\frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4+2\sqrt{3} ni \frac{3^{2}}{3^{2}} marotabaga ko'paytirish.

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

\frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} va \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9 hisob-kitobini qiling.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

3^{2} ni kengaytirish.

$$\frac{48+24\sqrt{3}}{9}$$