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

Results 1 to 4 of 4

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

- Joined
- Sep 2012
- From
- Kota
- Posts
- 73

## 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**?

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

- Joined
- Sep 2012
- From
- Kota
- Posts
- 73

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

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,026
- Thanks
- 844

## 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: .

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

- Joined
- Sep 2012
- From
- Kota
- Posts
- 73