Issolvi [1+1/sqrt{2}+1/2][1-1/sqrt{2}+1/2]

$$[ 1 + \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { 2 } ] [ 1 - \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { 2 } ]$$

Evalwa

$$\frac{7}{4}=1.75$$

Passi tas-Soluzzjonijiet

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

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

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

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

Ikkonverti 1 fi frazzjoni \frac{2}{2}.

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

Billi \frac{2}{2} u \frac{1}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Żid 2 u 1 biex tikseb 3.

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

Billi \frac{3}{2} u \frac{\sqrt{2}}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

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

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

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

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

Ikkonverti 1 fi frazzjoni \frac{2}{2}.

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

Billi \frac{2}{2} u \frac{1}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Żid 2 u 1 biex tikseb 3.

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

Billi \frac{3}{2} u \frac{\sqrt{2}}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{3+\sqrt{2}}{2}\times \frac{3+\sqrt{2}}{2}$$

Immultiplika \frac{3+\sqrt{2}}{2} u \frac{3+\sqrt{2}}{2} biex tikseb \left(\frac{3+\sqrt{2}}{2}\right)^{2}.

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

Biex tgħolli \frac{3+\sqrt{2}}{2} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(3+\sqrt{2}\right)^{2}.

$$\frac{9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}$$

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

$$\frac{9+6\sqrt{2}+2}{2^{2}}$$

Żid 9 u 2 biex tikseb 11.

$$\frac{11+6\sqrt{2}}{2^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{11+6\sqrt{2}}{4}$$

Fattur

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$