[(sqrt{2})^{2}*(2/sqrt{3})^2][(1/2)^2+4*1^2-2^2] eching

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

Baholash

$$\frac{2}{3}\approx 0,666666667$$

Yechim qadamlari

\sqrt{2} kvadrati – 2.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

2 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

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

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

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

4 hosil qilish uchun 4 va 1 ni ko'paytirish.

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

\frac{17}{4} olish uchun \frac{1}{4} va 4'ni qo'shing.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-2^{2}\right)$$

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

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-4\right)$$

\frac{1}{4} olish uchun \frac{17}{4} dan 4 ni ayirish.

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

\frac{1}{2} hosil qilish uchun 2 va \frac{1}{4} ni ko'paytirish.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

$$\frac{1}{2}\times \frac{4\times 3}{3^{2}}$$

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

$$\frac{1}{2}\times \frac{12}{3^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{1}{2}\times \frac{12}{9}$$

\frac{12}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}\times \frac{4}{3}$$

\frac{2}{3} hosil qilish uchun \frac{1}{2} va \frac{4}{3} ni ko'paytirish.

$$\frac{2}{3}$$

Omil

$$\frac{2}{3} = 0,6666666666666666$$