# There are 4 consicutive odd numbers which when multipliedtogetherthe answer is 9,009.what are the numbers

1
by juddrussel

2015-06-14T13:07:03+08:00

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Method 1:
We know from the divisibility rules that 9009 is divisible by 9 and 11 so by continuous division:
9   | 9009
11 | 1001
7   |  91
13
Therefore the 4 conscutive odd numbers are 7,9,11,13

Method 2:
We represent the numbers by x-3,x-1,x+1,x+3
(x-3)(x-1)(x+1)(x+3) = 9009
(x-3)(x+3)(x-1)(x+1) = 9009
(x²-9)(x²-1)=9009
x⁴-10x²+9=9009
x⁴-10x²-9000=0

We perform quadratic formula: (but we only take the plus)
x² = 10 + √(10²+36000) = 10 + √36100 = 10 + 190 = 200 = 100
2                        2                 2           2
x = √100 = 10

Therefore the numbers are 7,9,11,13