Issolvi {left(1+sqrt{3}right)}^2+{left(frac{sqrt{3}}{3}+1right)}^2=

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

Evalwa

$$\frac{8\left(\sqrt{3}+2\right)}{3}\approx 9.952135487$$

Passi Qosra tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(1+\sqrt{3}\right)^{2}.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Żid 1 u 3 biex tikseb 4.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{3}{3}.

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

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

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

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

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 4+2\sqrt{3} b'\frac{3^{2}}{3^{2}}.

$$\frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}}+\frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Billi \frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} u \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Agħmel il-multiplikazzjonijiet fi \left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

Agħmel il-kalkoli fi 36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

Espandi 3^{2}.

$$\frac{48+24\sqrt{3}}{9}$$

Espandi

$$\frac{8 \sqrt{3} + 16}{3} = 9.95213548685034$$

Passi Qosra tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(1+\sqrt{3}\right)^{2}.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Żid 1 u 3 biex tikseb 4.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{3}{3}.

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

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

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

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

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 4+2\sqrt{3} b'\frac{3^{2}}{3^{2}}.

$$\frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}}+\frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Billi \frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} u \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}}{3^{2}}$$

Agħmel il-multiplikazzjonijiet fi \left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

Agħmel il-kalkoli fi 36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

Espandi 3^{2}.

$$\frac{48+24\sqrt{3}}{9}$$