Question

Answer please friends with steps
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Answer 1

7,-2,-6,-1

-4, -3,1,4

0,-2,-3,3

-5,5,6,-8

Answer 2

Complete solution :

The given magic square is

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&\\ \cline{1-4}&&1&\\ \cline{1-4}0&-2&&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}\end{center}$

••• If a be the unknown number in the first column, by the given condition,

    7 + a + 0 + (- 5) = - 2

⇒ a + 2 = - 2

⇒ a = - 4

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&\\ \cline{1-4}-4&&1&\\ \cline{1-4}0&-2&&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If b be the unknown number in third column, by the given condition,

    - 6 + 1 + b + 6 = - 2

⇒ 1 + b = - 2

⇒ b = - 3

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&\\ \cline{1-4}-4&&1&\\ \cline{1-4}0&-2&-3&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If c be the unknown number in first diagonal, by given condition,

    7 + c + (- 3) + (- 8) = - 2

⇒ 7 + c - 3 - 8 = - 2

⇒ c - 4 = - 2

⇒ c = 2

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&\\ \cline{1-4}-4&2&1&\\ \cline{1-4}0&-2&-3&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If d be the unknown number in second diagonal, by given condition,

   (- 5) + (- 2) + 1 + e = - 2

⇒ - 5 - 2 + 1 + e = - 2

⇒ e - 6 = - 2

⇒ e = 4

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&4\\ \cline{1-4}-4&2&1&\\ \cline{1-4}0&-2&-3&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If f be the unknown number in second row, by given condition,

   (- 4) + 2 + 1 + f = - 2

⇒ - 4 + 2 + 1 + f = - 2

⇒ f - 1 = - 2

⇒ f = - 1

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&4\\ \cline{1-4}-4&2&1&-1\\ \cline{1-4}0&-2&-3&\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If g be the unknown number in third row, by given condition,

    0 + (- 2) + (- 3) + g = - 2

⇒ 0 - 2 - 3 + g = - 2

⇒ g - 5 = - 2

⇒ g = 3

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&&-6&4\\ \cline{1-4}-4&2&1&-1\\ \cline{1-4}0&-2&-3&3\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If h be the unknown number in first row, by given condition

    7 + h + (- 6) + 4 = - 2

⇒ 7 + h - 6 + 4 = - 2

⇒ h + 5 = - 2

⇒ h = - 7

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&-7&-6&4\\ \cline{1-4}-4&2&1&-1\\ \cline{1-4}0&-2&-3&3\\ \cline{1-4}-5&&6&-8\\ \cline{1-4}\end{array}$

••• If i be the unknown number in second column, by given condition,

   (- 7) + 2 + (- 2) + i = - 2

⇒ - 7 + 2 - 2 + i = - 2

⇒ - 7 + i = - 2

⇒ i = 5

Then, the magic square becomes

    $\begin{array}{|c|c|c|c|}\cline{1-4}7&\bf -7&-6&\bf 4\\ \cline{1-4}\bf -4&\bf 2&1&\bf -1\\ \cline{1-4}0&-2&\bf -3&\bf 3\\ \cline{1-4}-5&\bf 5&6&-8\\ \cline{1-4}\end{array}$