(sqrt{3})^2-2(1/2)^2-3/4(sqrt{2})^2-4(2/sqrt{3})^2 eching

$$( \sqrt { 3 } ) ^ { 2 } - 2 ( \frac { 1 } { 2 } ) ^ { 2 } - \frac { 3 } { 4 } ( \sqrt { 2 } ) ^ { 2 } - 4 ( \frac { 2 } { \sqrt { 3 } } ) ^ { 2 }$$

Baholash

$$-\frac{13}{3}\approx -4,333333333$$

Yechim qadamlari

\sqrt{3} kvadrati – 3.

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

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

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

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

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

\frac{5}{2} olish uchun 3 dan \frac{1}{2} ni ayirish.

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

\sqrt{2} kvadrati – 2.

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

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

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

1 olish uchun \frac{5}{2} dan \frac{3}{2} ni ayirish.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

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

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

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

$$1-\frac{4\times 12}{3^{2}}$$

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

$$1-\frac{48}{3^{2}}$$

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

$$1-\frac{48}{9}$$

\frac{48}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$1-\frac{16}{3}$$

-\frac{13}{3} olish uchun 1 dan \frac{16}{3} ni ayirish.

$$-\frac{13}{3}$$

Omil

$$-\frac{13}{3} = -4\frac{1}{3} = -4,333333333333333$$