Issolvi -1/4*({left(frac{5sqrt{10}-8}{3}right)}^2

$$- \frac{ 1 }{ 4 } \times ( { \left( \frac{ 5 \sqrt{ 10 } -8 }{ 3 } \right) }^{ 2 }$$

Evalwa

$$\frac{20\sqrt{10}}{9}-\frac{157}{18}\approx -1.694938533$$

Passi tas-Soluzzjonijiet

Biex tgħolli \frac{5\sqrt{10}-8}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$-\frac{1}{4}\times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}}$$

Immultiplika -\frac{1}{4} b'\frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-\left(5\sqrt{10}-8\right)^{2}}{4\times 3^{2}}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(5\sqrt{10}-8\right)^{2}.

$$\frac{-\left(25\left(\sqrt{10}\right)^{2}-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$\frac{-\left(25\times 10-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Immultiplika 25 u 10 biex tikseb 250.

$$\frac{-\left(250-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Żid 250 u 64 biex tikseb 314.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 3^{2}}$$

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

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 9}$$

Immultiplika 4 u 9 biex tikseb 36.

$$\frac{-\left(314-80\sqrt{10}\right)}{36}$$

Biex issib l-oppost ta' 314-80\sqrt{10}, sib l-oppost ta' kull terminu.

$$\frac{-314+80\sqrt{10}}{36}$$

Espandi

$$\frac{20 \sqrt{10}}{9} - \frac{157}{18} = -1.694938533$$

Passi tas-Soluzzjonijiet

Biex tgħolli \frac{5\sqrt{10}-8}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$-\frac{1}{4}\times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}}$$

Immultiplika -\frac{1}{4} b'\frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-\left(5\sqrt{10}-8\right)^{2}}{4\times 3^{2}}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(5\sqrt{10}-8\right)^{2}.

$$\frac{-\left(25\left(\sqrt{10}\right)^{2}-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$\frac{-\left(25\times 10-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Immultiplika 25 u 10 biex tikseb 250.

$$\frac{-\left(250-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Żid 250 u 64 biex tikseb 314.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 3^{2}}$$

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

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 9}$$

Immultiplika 4 u 9 biex tikseb 36.

$$\frac{-\left(314-80\sqrt{10}\right)}{36}$$

Biex issib l-oppost ta' 314-80\sqrt{10}, sib l-oppost ta' kull terminu.

$$\frac{-314+80\sqrt{10}}{36}$$