Lahenda frac{1-4sqrt{5}-3}{3-sqrt{5}-sqrt{5}+2}=

$$\frac { 1 - 4 \sqrt { 5 } - 3 } { 3 - \sqrt { 5 } - \sqrt { 5 } + 2 } =$$

Arvuta

$$-\frac{24\sqrt{5}}{5}-10\approx -20,733126292$$

Lahenduse etapid

Lahutage 3 väärtusest 1, et leida -2.

$$\frac{-2-4\sqrt{5}}{3-\sqrt{5}-\sqrt{5}+2}$$

Kombineerige -\sqrt{5} ja -\sqrt{5}, et leida -2\sqrt{5}.

$$\frac{-2-4\sqrt{5}}{3-2\sqrt{5}+2}$$

Liitke 3 ja 2, et leida 5.

$$\frac{-2-4\sqrt{5}}{5-2\sqrt{5}}$$

Ratsionaliseerige korrutades lugeja ja 5+2\sqrt{5} nimetaja \frac{-2-4\sqrt{5}}{5-2\sqrt{5}} nimetaja.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{\left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right)}$$

Mõelge valemile \left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Arvutage 2 aste 5 ja leidke 25.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\sqrt{5}\right)^{2}}$$

Laiendage \left(-2\sqrt{5}\right)^{2}.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

Arvutage 2 aste -2 ja leidke 4.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} ruut on 5.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\times 5}$$

Korrutage 4 ja 5, et leida 20.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-20}$$

Lahutage 20 väärtusest 25, et leida 5.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{5}$$

Rakendage distributiivsusomadus, korrutades avaldise -2-4\sqrt{5} iga liikme avaldise 5+2\sqrt{5} iga liikmega.

$$\frac{-10-4\sqrt{5}-20\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

Kombineerige -4\sqrt{5} ja -20\sqrt{5}, et leida -24\sqrt{5}.

$$\frac{-10-24\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

\sqrt{5} ruut on 5.

$$\frac{-10-24\sqrt{5}-8\times 5}{5}$$

Korrutage -8 ja 5, et leida -40.

$$\frac{-10-24\sqrt{5}-40}{5}$$

Lahutage 40 väärtusest -10, et leida -50.

$$\frac{-50-24\sqrt{5}}{5}$$