All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Quintic Expression (Posted on 2013-10-09) Difficulty: 2 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: Easy way out---hard way in | Comment 6 of 8 |
(In reply to Easy way out by Jer)

You say:

The expression becomes

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


NO
 If  c-d=0
 The expression becomes  27+0/0+0/0,

therefore you cannot assume c=d

  Posted by Ady TZIDON on 2013-10-11 02:14:56
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information