Consider all quadruples of real numbers (x1,x2,x3,x4), such that x1≤x2≤x3≤x4 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 x4, what is S,rounded to the nearest integer?
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Consider all quadruples of real numbers (x1,x2,x3,x4), such that x1≤x2≤x3≤x4 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 x4, what is S,rounded to the nearest integer?
1,2,3,4 are the subscripts of x
Hello, geniusgarvil!
Quote:
Consider all quadruples of real numbers, such that
and each of the four numbers plus the product of the other three equals 130.
Ifis the sum of all possible values of
, what is
We have: .
Since the four variables are completely interchangeable,
. . we conclude that: .
The first equation becomes: .
. . The only real root is: .
Therefore: .
I,don't know what's wrong in your solution, but the answer's incorrect.