Issolvi 2*2/-1+sqrt{5}

$$2 \times \frac{ 2 }{ -1+ \sqrt{ 5 } }$$

Evalwa

$$\sqrt{5}+1\approx 3.236067977$$

Passi tas-Soluzzjonijiet

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

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

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}.

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

Ikkwadra -1. Ikkwadra \sqrt{5}.

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

Naqqas 5 minn 1 biex tikseb -4.

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

Iddividi 2\left(-1-\sqrt{5}\right) b'-4 biex tikseb-\frac{1}{2}\left(-1-\sqrt{5}\right).

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

Uża l-propjetà distributtiva biex timmultiplika -\frac{1}{2} b'-1-\sqrt{5}.

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

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

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

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

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'\frac{1}{2}+\frac{1}{2}\sqrt{5}.

$$2\times \frac{1}{2}+2\times \frac{1}{2}\sqrt{5}$$

Annulla 2 u 2.

$$1+2\times \frac{1}{2}\sqrt{5}$$

Annulla 2 u 2.

$$1+\sqrt{5}$$

Fattur

$$\sqrt{5} + 1 = 3.236067977$$