Lntegers 0, -2, -3, -4, -5, -6, -7, -8, and -10 to fill in a 3 x 3 magic square so that every row, column, and diagonal has the same sum. The sum must be -15.

The given numbers are 0, -2, -3, -4, -5, -6, -7, -8, and -10.

Sum of all the integers is -45.

There are 9 places in 3x3 magic square, so divide -45 by 9, we have -45/9=-5.

Put the number -5 at the center place in the magic square.

Now, take the integer having the largest magnitude, i.e -10.

There are two positions to place -10, one is diagonal positions and the other is non-diagonal positions and to make sum = -15, the other number with -5 and -10 must be 0 as shown in the figure (i) and (ii).

Now, the row and column having 0 must have -8 and -7 to make sum -15, which disregards the possibility of -10 at the diagonal place ( figure (i)). So, proceeds with the places in figure (ii), the possible places of -8 and -7 have been shown in figure (iii).

Now, as the sum of diagonals = -15, so place -3 and -2 at diagonal positions and also place the remaining numbers -4 and -6 to make the sum of numbers in columns and rows -15 as shown in figure (iv).

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: