perplexus.info :: Just Math : Valid system of equations

Valid system of equations (Posted on 2020-10-16)

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)

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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(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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