Issolvi sqrt{2}+1-frac{1+sqrt{2}}{sqrt{2}+156}

$$\sqrt{ 2 } +1- \frac{ 1+ \sqrt{ 2 } }{ \sqrt{ 2 } +156 }$$

Evalwa

$$\frac{24179\sqrt{2}}{24334}+\frac{12090}{12167}\approx 2.398876869$$

Passi Qosra tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{1+\sqrt{2}}{\sqrt{2}+156} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}-156.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}+156\right)\left(\sqrt{2}-156\right)}$$

Ikkunsidra li \left(\sqrt{2}+156\right)\left(\sqrt{2}-156\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}.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}\right)^{2}-156^{2}}$$

Ikkwadra \sqrt{2}. Ikkwadra 156.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{2-24336}$$

Naqqas 24336 minn 2 biex tikseb -24334.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{-24334}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 1+\sqrt{2} b'kull terminu ta' \sqrt{2}-156.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+\left(\sqrt{2}\right)^{2}-156\sqrt{2}}{-24334}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+2-156\sqrt{2}}{-24334}$$

Żid -156 u 2 biex tikseb -154.

$$\sqrt{2}+1-\frac{\sqrt{2}-154-156\sqrt{2}}{-24334}$$

Ikkombina \sqrt{2} u -156\sqrt{2} biex tikseb -155\sqrt{2}.

$$\sqrt{2}+1-\frac{-155\sqrt{2}-154}{-24334}$$

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

$$\sqrt{2}+1-\frac{155\sqrt{2}+154}{24334}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika \sqrt{2}+1 b'\frac{24334}{24334}.

$$\frac{24334\left(\sqrt{2}+1\right)}{24334}-\frac{155\sqrt{2}+154}{24334}$$

Billi \frac{24334\left(\sqrt{2}+1\right)}{24334} u \frac{155\sqrt{2}+154}{24334} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right)}{24334}$$

Agħmel il-multiplikazzjonijiet fi 24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right).

$$\frac{24334\sqrt{2}[phone]\sqrt{2}-154}{24334}$$

Agħmel il-kalkoli fi 24334\sqrt{2}[phone]\sqrt{2}-154.

$$\frac{24179\sqrt{2}+24180}{24334}$$