Resol frac{(2^{2}2/3+34/7)^2+[22/3-34/7]^2}{(frac{8}{3})^2+[frac{25}{7}]^2}

$$\frac { ( 2 ^ { 2 } \frac { 2 } { 3 } + 3 \frac { 4 } { 7 } ) ^ { 2 } + [ 2 \frac { 2 } { 3 } - 3 \frac { 4 } { 7 } ] ^ { 2 } } { ( \frac { 8 } { 3 } ) ^ { 2 } + [ \frac { 25 } { 7 } ] ^ { 2 } }$$

Calcula

$$2$$

Passos de solució

Calculeu 2 elevat a 2 per obtenir 4.

$$\frac{\left(4\times \frac{2}{3}+\frac{3\times 7+4}{7}\right)^{2}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Multipliqueu 4 per \frac{2}{3} per obtenir \frac{8}{3}.

$$\frac{\left(\frac{8}{3}+\frac{3\times 7+4}{7}\right)^{2}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Multipliqueu 3 per 7 per obtenir 21.

$$\frac{\left(\frac{8}{3}+\frac{21+4}{7}\right)^{2}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Sumeu 21 més 4 per obtenir 25.

$$\frac{\left(\frac{8}{3}+\frac{25}{7}\right)^{2}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Sumeu \frac{8}{3} més \frac{25}{7} per obtenir \frac{131}{21}.

$$\frac{\left(\frac{131}{21}\right)^{2}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Calculeu \frac{131}{21} elevat a 2 per obtenir \frac{17161}{441}.

$$\frac{\frac{17161}{441}+\left(\frac{2\times 3+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Multipliqueu 2 per 3 per obtenir 6.

$$\frac{\frac{17161}{441}+\left(\frac{6+2}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Sumeu 6 més 2 per obtenir 8.

$$\frac{\frac{17161}{441}+\left(\frac{8}{3}-\frac{3\times 7+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Multipliqueu 3 per 7 per obtenir 21.

$$\frac{\frac{17161}{441}+\left(\frac{8}{3}-\frac{21+4}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Sumeu 21 més 4 per obtenir 25.

$$\frac{\frac{17161}{441}+\left(\frac{8}{3}-\frac{25}{7}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Resteu \frac{8}{3} de \frac{25}{7} per obtenir -\frac{19}{21}.

$$\frac{\frac{17161}{441}+\left(-\frac{19}{21}\right)^{2}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Calculeu -\frac{19}{21} elevat a 2 per obtenir \frac{361}{441}.

$$\frac{\frac{17161}{441}+\frac{361}{441}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Sumeu \frac{17161}{441} més \frac{361}{441} per obtenir \frac{17522}{441}.

$$\frac{\frac{17522}{441}}{\left(\frac{8}{3}\right)^{2}+\left(\frac{25}{7}\right)^{2}}$$

Calculeu \frac{8}{3} elevat a 2 per obtenir \frac{64}{9}.

$$\frac{\frac{17522}{441}}{\frac{64}{9}+\left(\frac{25}{7}\right)^{2}}$$

Calculeu \frac{25}{7} elevat a 2 per obtenir \frac{625}{49}.

$$\frac{\frac{17522}{441}}{\frac{64}{9}+\frac{625}{49}}$$

Sumeu \frac{64}{9} més \frac{625}{49} per obtenir \frac{8761}{441}.

$$\frac{\frac{17522}{441}}{\frac{8761}{441}}$$

Dividiu \frac{17522}{441} per \frac{8761}{441} multiplicant \frac{17522}{441} pel recíproc de \frac{8761}{441}.

$$\frac{17522}{441}\times \frac{441}{8761}$$

Multipliqueu \frac{17522}{441} per \frac{441}{8761} per obtenir 2.

$$2$$

Factoritzar

$$2$$