All about
flooble

fun stuff

Get a free chatterbox

Free JavaScript

Avatars
perplexus
dot
info
Home
>
Just Math
Valid system of equations (
Posted on 20201016
)
Find minimal value of a such that system
(x1)
^{1/2}
+(y1)
^{1/2}
+(z1)
^{1/2}
=a1
(x+1)
^{1/2}
+(y+1)
^{1/2}
+(z+1)
^{1/2}
=a+1
has solution in set of real numbers.
No Solution Yet
Submitted by
Danish Ahmed Khan
Rating:
3.0000
(1 votes)
Comments: (
Back to comment list
 You must be logged in to post comments.
)
Solution
 Comment 1 of 3
A little playing around with Desmos convinced me the minimal value of a occurs when x=y=z
https://www.desmos.com/calculator/gxbltdooft
Which simplifies the system to
3(x1)
^{1/2}
=a1
3(x+1)
^{1/2}
=a+1
This is easily solved to find a=4.5
x=y=z=85/36
Posted by
Jer
on 20201016 08:25:17
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 (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
blackjack
flooble's webmaster puzzle
Copyright © 2002  2024 by
Animus Pactum Consulting
. All rights reserved.
Privacy Information