1,2,3,4 are the subscripts of x

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- Mar 19th 2013, 01:58 AM #1

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## Cyclically 130

Consider all quadruples of real numbers (*x*1,*x*2,*x*3,*x*4), such that*x*1≤*x*2≤*x*3≤*x*4 and each of the four numbers plus the product of the other three equals 130. If*S*is the sum of all possible values of*x*4, what is*S*,**rounded to the nearest integer**?

- Mar 19th 2013, 01:59 AM #2

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- Mar 19th 2013, 07:53 AM #3

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## Re: Cyclically 130

Hello, geniusgarvil!

Consider all quadruples of real numbers , such that

and each of the four numbers plus the product of the other three equals 130.

If is the sum of all possible values of , what is ? .(Round to nearest integer.)

We have: .

Since the four variables are completely interchangeable,

. . we conclude that: .

The first equation becomes: .

. . The only real root is: .

Therefore: .

- Mar 19th 2013, 07:00 PM #4

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