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)

(In reply to Easy way out by Jer)

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

Posted by Ady TZIDON on 2013-10-11 02:14:56