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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: (
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)
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(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
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