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

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

Evalwa

$$-\frac{13}{3}\approx -4.333333333$$

Passi tas-Soluzzjonijiet

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Ikkalkula \frac{1}{2} bil-power ta' 2 u tikseb \frac{1}{4}.

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

Immultiplika 2 u \frac{1}{4} biex tikseb \frac{1}{2}.

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

Naqqas \frac{1}{2} minn 3 biex tikseb \frac{5}{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Immultiplika \frac{3}{4} u 2 biex tikseb \frac{3}{2}.

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

Naqqas \frac{3}{2} minn \frac{5}{2} biex tikseb 1.

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

Irrazzjonalizza d-denominatur tal-\frac{2}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Biex tgħolli \frac{2\sqrt{3}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Esprimi 4\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}} bħala frazzjoni waħda.

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

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

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

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Immultiplika 4 u 3 biex tikseb 12.

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

Immultiplika 4 u 12 biex tikseb 48.

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

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

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

Naqqas il-frazzjoni \frac{48}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

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

Naqqas \frac{16}{3} minn 1 biex tikseb -\frac{13}{3}.

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

Fattur

$$-\frac{13}{3} = -4\frac{1}{3} = -4.333333333333333$$