frac{(frac{sqrt{3}}{1})^{2}+4*(1/sqrt{2})^2+3*(2/sqrt{3})^2+5*0^2}{2+2-(sqrt{3})^2} eching

$$\frac { ( \frac { \sqrt { 3 } } { 1 } ) ^ { 2 } + 4 \times ( \frac { 1 } { \sqrt { 2 } } ) ^ { 2 } + 3 \times ( \frac { 2 } { \sqrt { 3 } } ) ^ { 2 } + 5 \times 0 ^ { 2 } } { 2 + 2 - ( \sqrt { 3 } ) ^ { 2 } }$$

Baholash

$$9$$

Yechim qadamlari

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$\frac{\left(\sqrt{3}\right)^{2}+4\times \left(\frac{1}{\sqrt{2}}\right)^{2}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{3+4\times \left(\frac{1}{\sqrt{2}}\right)^{2}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{3+4\times \left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{3+4\times \left(\frac{\sqrt{2}}{2}\right)^{2}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{3+4\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

4\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} ni yagona kasrga aylantiring.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+3\times \left(\frac{2}{\sqrt{3}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\frac{2}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+3\times \left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+3\times \left(\frac{2\sqrt{3}}{3}\right)^{2}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+3\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

3\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}} ni yagona kasrga aylantiring.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{3\times \left(2\sqrt{3}\right)^{2}}{3^{2}}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{\left(2\sqrt{3}\right)^{2}}{3}+5\times 0^{2}}{2+2-\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{\left(2\sqrt{3}\right)^{2}}{3}+5\times 0}{2+2-\left(\sqrt{3}\right)^{2}}$$

0 hosil qilish uchun 5 va 0 ni ko'paytirish.

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{\left(2\sqrt{3}\right)^{2}}{3}+0}{2+2-\left(\sqrt{3}\right)^{2}}$$

3 olish uchun 3 va 0'ni qo'shing.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

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

$$\frac{3+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{12}{3}}{2+2-\left(\sqrt{3}\right)^{2}}$$

4 ni olish uchun 12 ni 3 ga bo‘ling.

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

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

$$\frac{7+\frac{4\left(\sqrt{2}\right)^{2}}{2^{2}}}{2+2-\left(\sqrt{3}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{7+\frac{4\times 2}{2^{2}}}{2+2-\left(\sqrt{3}\right)^{2}}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{7+\frac{8}{2^{2}}}{2+2-\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{7+\frac{8}{4}}{2+2-\left(\sqrt{3}\right)^{2}}$$

2 ni olish uchun 8 ni 4 ga bo‘ling.

$$\frac{7+2}{2+2-\left(\sqrt{3}\right)^{2}}$$

9 olish uchun 7 va 2'ni qo'shing.

$$\frac{9}{2+2-\left(\sqrt{3}\right)^{2}}$$

4 olish uchun 2 va 2'ni qo'shing.

$$\frac{9}{4-\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{9}{4-3}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{9}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$9$$

Omil

$$3^{2}$$