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

Home > Just Math
Quartic Sum Determination (Posted on 2015-07-05) Difficulty: 3 of 5
A, B and C are roots of the equation: x3 - 8x2 + 5x +12 = 0

Without solving the above equation, find the value of :
A4 + B4 + C4

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution Comment 1 of 1

Equating coefficients in

(x - A)(x - B)(x - C) = x3 - 8x2 + 5x + 12    gives:


A + B + C = 8,    AB + BC + CA = 5,    ABC = -12.

Using these values in the following identity:

A4 + B4 + C4 = (A + B + C)4 – 4(A + B + C)2(AB + BC + CA)

                        +2(AB + BC + CA)2 + 4ABC(A + B + C)

A4 + B4 + C4      = 84 - 4*82*5 + 2*52 - 4*12*8

                        = 2482




  Posted by Harry on 2015-07-05 17:25:49
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 (4)
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