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Valid system of equations (Posted on 2020-10-16) Difficulty: 3 of 5
Find minimal value of a such that system

(x-1)1/2+(y-1)1/2+(z-1)1/2=a-1
(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 2
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(x-1)1/2=a-1
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 2020-10-16 08:25:17
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