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

Home > Numbers
Sum of powers (Posted on 2015-11-18) Difficulty: 2 of 5
Given a+b=1 & a^2+b^2 =25,

Find a^4+b^4, without solving for a and b.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 3
Square the first equation
a^2+2ab+b^2=1
2ab+25=1
ab=-12
(ab)^2=144

Square the second equation
a^4+2(ab)^2+b^4=625
a^4+b^4=625-2(ab)^2
a^4+b^4=625-2(144)=337.

p.s.
Squaring -12 bothered me, so to confirm the solution I did solve for a and b with a graph: (4,-3) or (-3,4).  And indeed 3^4+4^4=337.

  Posted by Jer on 2015-11-18 08:33:17
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 (3)
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