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

Home > Just Math
Sum and Square Root Sum (Posted on 2010-09-25) Difficulty: 3 of 5
Determine all possible pair(s) (x,y) of real numbers that satisfy this set of equations:

x+y = 23, and:

√(x2 + 12*y) + √(y2 + 12*x) = 33

*** For an extra challenge, solve this puzzle without the aid of an online equation solver or a computer program.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
analytical solution | Comment 1 of 3

x+y=23 thus y=23-x, substituting this into the second we get
(x-12x+276) + (x-34x+529) = 33 squaring both sides we get
2x-46x+805+2( (x-12x+276)*(x-34x+529) ) = 1089
(x-12x+276)*(x-34x+529) = (x-23x-142)
thus x=10 and y=13 or
x=13 and y=10
thus the only real solutions are
(10,13) and (13,10)

  Posted by Daniel on 2010-09-25 13:36:26
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information