Question

Descubra o valor de X no quadrado mágico e encontre o valor da SOMA das colunas, das linhas e das diagonais. Lembre-se que a soma das colunas, das linhas e das diagonais em um quadrado mágico é sempre a mesma. Reescreva o quadrado com os valores correspondentes



pfv me ajudem​

Answer 1

Valor de x = 4

Soma das colunas, linhas e diagonais =  30

                                  Quadrado mágico  

• Um quadrado mágico é uma tabela quadrada de lado n, onde a soma dos números das  linhas, das colunas e das diagonais é constante, sendo que nenhum destes números se  repete.

Na expressão     $\dfrac{x^2}{2} + 9$    podemos inferir que o número procurador para x tem que ser um número par, pois se x for impar o resultado não será um número inteiro.

Testar para x = 2 na coluna na primeira linha e coluna do meio.

$\large\begin{array}{|c|}\cline{1-3}\\~~2x^2-20~~\\\\\cline{1-3}\\~~3x+1~~\\\\\cline{1-3}\\~~5~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~3~~\\\\\cline{1-3}\\~~2x+2~~\\\\\cline{1-3}\\~~x^2/2\,+\,9~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~x^2-1~~\\\\\cline{1-3}\\~~7~~\\\\\cline{1-3}\\~~2x~~\\\\\cline{1-3}\end{array}$  $\large\begin{array}{|c|}\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~--~~\\\\\cline{1-3}\\~~--~~\\\\\cline{1-3}\\~~--~~\\\\\cline{1-3}\end{array}$

$\large\begin{array}{|c|}\cline{1-3}\\~~~~~--~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~--~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~--~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~--~~\\\\\cline{1-3}\end{array}$

===

$2x + 2 = 2 . 2 + 2 = 6$

$\dfrac{2^2}{2} + 9 ~= ~~ \dfrac{2^2}{2} + 9~~= ~~ \dfrac{4}{2} + 9~~=~~\ 2 + 9 => 11}$

Com os valor encontrados, substituir o valor de x.

$\large\begin{array}{|c|}\cline{1-3}\\~~~~~~-12~~~~~~\\\\\cline{1-3}\\~~3x+1~~\\\\\cline{1-3}\\~~~~~~5~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~3~~\\\\\cline{1-3}\\~~~~~6~~~~~~\\\\\cline{1-3}\\~~11~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~3~~~~~~\\\\\cline{1-3}\\~~7~~\\\\\cline{1-3}\\~~2x~~\\\\\cline{1-3}\end{array}$ $\large\begin{array}{|c|}\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~-6~~\\\\\cline{1-3}\\~~~~~~\\\\\cline{1-3}\\~~~~~~\\\\\cline{1-3}\end{array}$

$\large\begin{array}{|c|}\cline{1-3}\\~~~~~~~~~~~~~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~~20~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~~~~~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~~~~~~\\\\\cline{1-3}\end{array}$

Para x = 2 não é solução do problema.

====

Para x = 4

$2x^2 - 10 ~~~= 2.4^2 - 20 ~~~= 2. 16 - 20~~ = 32 - 30 => 12$

$x^2 - 1 ~~= ~~4^2 - 1 ~~= ~~16 - 1 ~~=> 15$

$3 . 4 + 1 ~~= ~~3 . 4 + 1 ~~= ~~ 12 + 1 ~~=> 13$

$2. 4 + 2 ~~= ~~2.4 + 2 = ~~8 + 2 ~~=> 10$

$\dfrac{x^2}{2} + 9 ~~= ~~ \dfrac{4^2}{2} + 9 ~~= ~~ \dfrac{16} {2} + 9 ~~= ~~ 8 + 9 ~~=> 17$

===

Substituir os valores de x no quadrado mágico.

$\large\begin{array}{|c|}\cline{1-3}\\~~~~~~~12~~~~~~\\\\\cline{1-3}\\~~~~13~~~~\\\\\cline{1-3}\\~~~~~~5~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~3~~\\\\\cline{1-3}\\~~~~~10~~~~~~\\\\\cline{1-3}\\~~17~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~15~~~~~~\\\\\cline{1-3}\\~~7~~\\\\\cline{1-3}\\~~8~~\\\\\cline{1-3}\end{array}$ $\large\begin{array}{|c|}\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~30~~\\\\\cline{1-3}\\~~30~~\\\\\cline{1-3}\\~~~30~~\\\\\cline{1-3}\end{array}$

$\large\begin{array}{|c|}\cline{1-3}\\~~~~~~~30~~~~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~~30~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~30~~~~~\\\\\cline{1-3}\end{array}\begin{array}{|c|}\cline{1-3}\\~~~~30~~~\\\\\cline{1-3}\end{array}$

===