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)

To maintain distinctness of the variables, setting only d=0 yields (as one possible answer): [a,b,c,d] = [5,2,-4,0]

Posted by Bryan on 2013-10-09 14:59:57