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For each positive integer k, the quantity

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For each positive integer k, the quantity [#permalink] New post 07 May 2013, 01:13
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1. For each positive integer k, the quantity x_k is defined such that x_k = x_{k+1} * ( x_{k+2})^3

In addition, x_3 = 1. In the table, select values for x_1 and x_4 that are jointly compatible with these conditions. Select only two values, one in each column.


x_1 -- x_4
------------------------------- 0
------------------------------- 2
------------------------------- 5
------------------------------- 8
------------------------------- 16
------------------------------- 64
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Re: For each positive integer k, the quantity [#permalink] New post 07 May 2013, 10:07
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Bunuel wrote:
1. For each positive integer k, the quantity x_k is defined such that x_k = x_{k+1} * ( x_{k+2})^3

In addition, x_3 = 1. In the table, select values for x_1 and x_4 that are jointly compatible with these conditions. Select only two values, one in each column.


x_1 -- x_4
------------------------------- 0
------------------------------- 2
------------------------------- 5
------------------------------- 8
------------------------------- 16
------------------------------- 64


From the above it can be deduced, that x1 = x2 = (x4)^3. Hence, for values of x1, x4 only 2,8 satisfy the same. If the above values apply, I believe the expression x-k cannot be said always an integer. since x-5 = (1/2)^(1/3). But since the question mentions it a 'quantity', it seems that fits the question as well.

Please correct me if I am wrong :)

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Re: For each positive integer k, the quantity [#permalink] New post 16 May 2013, 19:18
X3 = 1
therefore x1=x2*1 or x1=x2 and
x2 = 1*(x4)^3
X1 = (x4)^3
only combinations for x1 and x4 where x1 can be cube of x4 is 8 for x1 and 2 for x4

And X1 = 8 / X4 = 2
Re: For each positive integer k, the quantity   [#permalink] 16 May 2013, 19:18
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