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RideAnS [48]
3 years ago
7

What is the answer for a magic square for the number 18?

Mathematics
2 answers:
Tanzania [10]3 years ago
6 0
The square of 18 is 9 because square = 2, so 18 ÷ 2 = 9. I hope this helps you.
Evgesh-ka [11]3 years ago
6 0
Hello,

32 solutions:

 1
|  1|  9|  8|
|  4|---|  3|
|  7|---|  5|
|  6| 10|  2|
---------------------
 2
|  1|  9|  8|
|  4|---|  5|
|  7|---|  3|
|  6| 10|  2|
---------------------
 3
|  1|  9|  8|
|  7|---|  3|
|  4|---|  5|
|  6| 10|  2|
---------------------
 4
|  1|  9|  8|
|  7|---|  5|
|  4|---|  3|
|  6| 10|  2|
---------------------
 5
|  2| 10|  6|
|  3|---|  1|
|  8|---|  7|
|  5|  9|  4|
---------------------
 6
|  2| 10|  6|
|  3|---|  4|
|  5|---|  7|
|  8|  9|  1|
---------------------
 7
|  2| 10|  6|
|  3|---|  7|
|  5|---|  4|
|  8|  9|  1|
---------------------
 8
|  2| 10|  6|
|  3|---|  7|
|  8|---|  1|
|  5|  9|  4|
---------------------
 9
|  2| 10|  6|
|  5|---|  4|
|  3|---|  7|
|  8|  9|  1|
---------------------
 10
|  2| 10|  6|
|  5|---|  7|
|  3|---|  4|
|  8|  9|  1|
---------------------
 11
|  2| 10|  6|
|  8|---|  1|
|  3|---|  7|
|  5|  9|  4|
---------------------
 12
|  2| 10|  6|
|  8|---|  7|
|  3|---|  1|
|  5|  9|  4|
---------------------
 13
|  4|  9|  5|
|  1|---|  3|
|  7|---|  8|
|  6| 10|  2|
---------------------
 14
|  4|  9|  5|
|  1|---|  8|
|  7|---|  3|
|  6| 10|  2|
---------------------
 15
|  4|  9|  5|
|  7|---|  3|
|  1|---|  8|
|  6| 10|  2|
---------------------
 16
|  4|  9|  5|
|  7|---|  8|
|  1|---|  3|
|  6| 10|  2|
---------------------
 17
|  5|  9|  4|
|  3|---|  1|
|  8|---|  7|
|  2| 10|  6|
---------------------
 18
|  5|  9|  4|
|  3|---|  7|
|  8|---|  1|
|  2| 10|  6|
---------------------
 19
|  5|  9|  4|
|  8|---|  1|
|  3|---|  7|
|  2| 10|  6|
---------------------
 20
|  5|  9|  4|
|  8|---|  7|
|  3|---|  1|
|  2| 10|  6|
---------------------
 21
|  6| 10|  2|
|  1|---|  3|
|  7|---|  8|
|  4|  9|  5|
---------------------
 22
|  6| 10|  2|
|  1|---|  8|
|  7|---|  3|
|  4|  9|  5|
---------------------
 23
|  6| 10|  2|
|  4|---|  3|
|  7|---|  5|
|  1|  9|  8|
---------------------
 24
|  6| 10|  2|
|  4|---|  5|
|  7|---|  3|
|  1|  9|  8|
---------------------
 25
|  6| 10|  2|
|  7|---|  3|
|  1|---|  8|
|  4|  9|  5|
---------------------
 26
|  6| 10|  2|
|  7|---|  3|
|  4|---|  5|
|  1|  9|  8|
---------------------
 27
|  6| 10|  2|
|  7|---|  5|
|  4|---|  3|
|  1|  9|  8|
---------------------
 28
|  6| 10|  2|
|  7|---|  8|
|  1|---|  3|
|  4|  9|  5|
---------------------
 29
|  8|  9|  1|
|  3|---|  4|
|  5|---|  7|
|  2| 10|  6|
---------------------
 30
|  8|  9|  1|
|  3|---|  7|
|  5|---|  4|
|  2| 10|  6|
---------------------
 31
|  8|  9|  1|
|  5|---|  4|
|  3|---|  7|
|  2| 10|  6|
---------------------
 32
|  8|  9|  1|
|  5|---|  7|
|  3|---|  4|
|  2| 10|  6|
---------------------


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Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

<h3>Step 1</h3>

Write the equation in standard form.

  4x³ -16x² -84x = 0

<h3>Step 2</h3>

Factor out the common factor from all terms.

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<h3>Step 3</h3>

Compare to the factored form of a quadratic:

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This tells you the constants 'a' and 'b' in the factors can be found by considering ...

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  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

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The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

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<h3>Step 4</h3>

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

<h3>Step 5</h3>

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

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