Question

sabe-se que a soma de cada linha, coluna e diagonal é igual a 15.

Answer 1

Olá!

Se cada linha, coluna e diagonal é igual a 15, então basta fazer a soma:

1ª linha:

$5 + x + \frac{16}{6} + \frac{9}{2} = 15 \\ \\ \frac{30+6x+16+27 }{6} = 15 \\ \\ \frac{73 + 6x}{6} = 15 \\ \\ 73 + 6x = 15 * 6 \\ \\ 6x = 90 - 73 \\ \\ x = \frac{17}{6}$

4ª coluna:

$\frac{9}{2} + x + \frac{26}{6} + \frac{5}{2}= 15 \\ \\ \frac{27 + 6x + 26 + 15}{6} = 15 \\ \\ \frac{68 + 6x}{6} = 15 \\ \\ 68 + 6x = 15 * 6 \\ \\ 6x = 90 - 68 \\ \\ x = \frac{22}{6}$

2ª linha:
$x + \frac{25}{6} + 4 + \frac{22}{6} = 15 \\ \\ \frac{6x + 25 + 24 + 22 }{6} =15 \\ \\ \frac{6x+71}{6} = 15 \\ \\ 6x + 71 = 15 * 6 \\ \\ 6x = 90- 71 \\ \\ x = \frac{19}{6}$




Diagonal: 

$5 + \frac{25 }{6} + x + \frac{5}{2} = 15 \\ \\ \frac{30 + 25 + 6x + 15}{6}=15 \\ \\ \frac{70 + 6x}{6} = 15 \\ \\ 70 + 6x = 15 * 6 \\ \\ 6x = 90 - 70 \\ \\ x = \frac{20}{6}$


3ª linha:

$x + \frac{7}{2} + \frac{20}{6} + \frac{26}{6} = 15 \\ \\ \frac{6x + 21 + 20 + 26}{6} = 15 \\ \\ \frac{6x + 67}{6} = 15 \\\\ 6x + 67 = 15 * 6\\\\ 6x = 90 - 67\\\\ x = \frac{23}{6}$


2ª coluna:

$\frac{17}{6} + \frac{25}{6} + \frac{7}{2} + x = 15\\\\ \frac{17+25+21+6x}{6}=15 \\\\ \frac{63 + 6x}{6} = 15\\\\ 63 + 6x = 15 *6\\\\ 6x = 90 - 63\\\\ x = \frac{27}{6}$


4ª linha:

$3 + \frac{27}{6} + x + \frac{5}{2} = 15 \\\\ \frac{18+27+6x+15}{6} = 15\\\\ \frac{60+6x}{6} =15\\\\ 60 + 6x = 15 * 6\\\\ 6x = 90 - 60\\\\ x= \frac{30}{6} \\\\ x = 5$

Portanto a tabela ficará assim:

$\frac{5}{1} | \frac{17}{6}| \frac{16}{6}| \frac{9}{2}\\\\ \frac{19}{6}| \frac{25}{6} | \frac{4}{1} | \frac{22}{6}\\\\ \frac{23}{6} | \frac{7}{2}| \frac{20}{6}| \frac{26}{6}\\\\ \frac{3}{1}| \frac{27}{6} | \frac{5}{1} | \frac{5}{2}$


Espero ter ajudado, abraço!