Issolvi frac{3-sqrt{2}}{(1-sqrt{5}}

$$\frac{ 3- \sqrt{ 2 } }{ (1- \sqrt{ 5 } }$$

Evalwa

$$\frac{\sqrt{2}+\sqrt{10}-3\sqrt{5}-3}{4}\approx -1.282928177$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{3-\sqrt{2}}{1-\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-1+\sqrt{5}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}$$

Ikkunsidra li \left(1-\sqrt{5}\right)\left(1+\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}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{1^{2}-\left(\sqrt{5}\right)^{2}}$$

Ikkwadra 1. Ikkwadra \sqrt{5}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{1-5}$$

Naqqas 5 minn 1 biex tikseb -4.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{-4}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 3-\sqrt{2} b'kull terminu ta' 1+\sqrt{5}.

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

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

$$\frac{3+3\sqrt{5}-\sqrt{2}-\sqrt{10}}{-4}$$

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

$$\frac{-3-3\sqrt{5}+\sqrt{2}+\sqrt{10}}{4}$$