Issolvi frac{sqrt{5}}{sqrt{2}-sqrt{5}}

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

Evalwa

$$\frac{-\sqrt{10}-5}{3}\approx -2.72075922$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{2}-\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}+\sqrt{5}.

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

Ikkunsidra li \left(\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra \sqrt{2}. Ikkwadra \sqrt{5}.

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

Naqqas 5 minn 2 biex tikseb -3.

$$\frac{\sqrt{5}\left(\sqrt{2}+\sqrt{5}\right)}{-3}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{5} b'\sqrt{2}+\sqrt{5}.

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

Biex timmultiplika \sqrt{5} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

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

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{\sqrt{10}+5}{-3}$$

Immultiplika kemm in-numeratur u kif ukoll id-denominatur b’-1.

$$\frac{-\sqrt{10}-5}{3}$$