Issolvi 3-4/3+sqrt{5}

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

Evalwa

$$\sqrt{5}\approx 2.236067977$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{4}{3+\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-3-\sqrt{5}.

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

Ikkunsidra li \left(3+\sqrt{5}\right)\left(3-\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}.

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

Ikkwadra 3. Ikkwadra \sqrt{5}.

$$3-\frac{4\left(3-\sqrt{5}\right)}{9-5}$$

Naqqas 5 minn 9 biex tikseb 4.

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

Annulla 4 u 4.

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

Biex issib l-oppost ta' 3-\sqrt{5}, sib l-oppost ta' kull terminu.

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

L-oppost ta' -\sqrt{5} huwa \sqrt{5}.

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

Naqqas 3 minn 3 biex tikseb 0.

$$\sqrt{5}$$