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 Quintic Expression (Posted on 2013-10-09)
Let a,b,c and d be distinct real numbers such that

a+b+c+d=3
a2+b2+c2+d2=45

Find the value of the expression
```       a5                b5                c5                d5
--------------- + --------------- + --------------- + --------------
(a-b)(a-c)(a-d)   (b-a)(b-c)(b-d)   (c-a)(c-b)(c-d)   (d-a)(d-b)(d-c)
```

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 4.0000 (1 votes)

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 Easy way out | Comment 1 of 8
The equations don't give enough info to actually find the values of the variables.  If we are told the expression has a definite value then all we need are values of the variables that fit the equations.

So lets let c=0 and d=0.
a+b=3
a^2+b^2=45
One solution is a=6, b=-3

The expression becomes
6^5/(9*6*6)+(-3)^5/(-9*-3*-3) = 27

[If this value depends on my choice of c and d, then I haven't really answered the question.  But I suspect it doesn't.]

 Posted by Jer on 2013-10-09 11:39:22

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