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

Home > Just Math
No fractions (Posted on 2020-09-19) Difficulty: 3 of 5
Find all integer solutions of:

x2+y2+ z2=2x-3z+5
x2+y2+3x=2

Any remarks?

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 1
(x,y,z)
 ( -1 , +/- 2 , -1 )
 ( -1 , +/- 2 , -2 )
 ( -1 , +/- 2 , -1 )
 ( -1 , +/- 2 , -2 )
 
 
(1) x^2+y^2+ z^2 = 2x-3z+5
(2) x^2+y^2+3x   = 2

subtract (2) from (1)
z^2 - 3x  = 2x-3z+3
z^2 + 3z -(5x+3) = 0

z = [-3 +/- sqrt(9+4(5x+3))]/2
z = -1.5 +/- [sqrt(20x + 21)]/2

If x is -1, then z = {-1 or -2}
For any other values of x, at least those which make
  20x + 21 a square, per Eqn (2), y^2 is negative
     y^2  = 2 - 3x - x^2

So the above are the only integer values

Edited on September 19, 2020, 11:41 am
  Posted by Larry on 2020-09-19 11:40:52

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information