Answer :
Odd number is: (2n-1), (2n+1), (2n+3), (2n+x),... where x x changes every two
(2n-1)(2n+1)=(2n+3)(2n+5)-64
[tex]4n^2-1=4n^2+10n+6n+15-64[/tex]
16n=48|:16
n=3
Now we substitute to (2n-1), (2n+1), (2n+3), (2n+5):
2n-1 = 2*3-1=5
2n+1 = 2*3+1=7
2n+3 = 2*3+3=9
2n+5 = 2*3+5=11
5,7,9,11
(2n-1)(2n+1)=(2n+3)(2n+5)-64
[tex]4n^2-1=4n^2+10n+6n+15-64[/tex]
16n=48|:16
n=3
Now we substitute to (2n-1), (2n+1), (2n+3), (2n+5):
2n-1 = 2*3-1=5
2n+1 = 2*3+1=7
2n+3 = 2*3+3=9
2n+5 = 2*3+5=11
5,7,9,11
If there are such numbers, then they can be written as 'x', (x + 2), (x + 4), and (x + 6).
Now, the problem says that x(x+2) + 64 = (x+4) (x+6)
Expand each side:
x² + 2x + 64 = x² + 10x + 24
Subtract (x² + 24) from each side:
2x + 40 = 10x
Subtract 2x from each side:
40 = 8x
Divide each side by 8 :
x = 5
The numbers are 5, 7, 9, and 11.
(5 x 7) + 64 = 35 + 64 = 99 and 9 x 11 = 99 . yay !
Now, the problem says that x(x+2) + 64 = (x+4) (x+6)
Expand each side:
x² + 2x + 64 = x² + 10x + 24
Subtract (x² + 24) from each side:
2x + 40 = 10x
Subtract 2x from each side:
40 = 8x
Divide each side by 8 :
x = 5
The numbers are 5, 7, 9, and 11.
(5 x 7) + 64 = 35 + 64 = 99 and 9 x 11 = 99 . yay !
