Issolvi 1/2+sqrt{3}+|sin30^circ-1|

$$\frac { 1 } { 2 + \sqrt { 3 } } + | \sin 30 ^ { \circ } - 1 |$$

Evalwa

$$\frac{5}{2}-\sqrt{3}\approx 0.767949192$$

Passi tas-Soluzzjonijiet

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

$$\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+|\sin(30)-1|$$

Ikkunsidra li \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\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}.

$$\frac{2-\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+|\sin(30)-1|$$

Ikkwadra 2. Ikkwadra \sqrt{3}.

$$\frac{2-\sqrt{3}}{4-3}+|\sin(30)-1|$$

Naqqas 3 minn 4 biex tikseb 1.

$$\frac{2-\sqrt{3}}{1}+|\sin(30)-1|$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$2-\sqrt{3}+|\sin(30)-1|$$

Ikseb il-valur ta’ \sin(30) mit-tabella tal-valuri trigonometriċi.

$$2-\sqrt{3}+|\frac{1}{2}-1|$$

Naqqas 1 minn \frac{1}{2} biex tikseb -\frac{1}{2}.

$$2-\sqrt{3}+|-\frac{1}{2}|$$

Il-valur assolut ta' numru reali a huwa a meta a\geq 0, jew -a meta a<0. Il-valur assolut ta' -\frac{1}{2} huwa \frac{1}{2}.

$$2-\sqrt{3}+\frac{1}{2}$$

Żid 2 u \frac{1}{2} biex tikseb \frac{5}{2}.

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