System of equations.

For discussing Olympiad Level Algebra (and Inequality) problems
jagdish
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Location: India (Himanchal Pradesh)

System of equations.

Unread post by jagdish » Wed Jan 04, 2012 1:58 am

solve all Real solution of System of equations

$x+y=\sqrt{4z-1}$

$y+z=\sqrt{4x-1}$

$z+x=\sqrt{4y-1}$
jagdish

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Moon
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Re: System of equations.

Unread post by Moon » Tue Jan 10, 2012 11:55 pm

With some work you can prove that $x=y=z=1/2$ is the only solution.
Substitution like $x=a+\frac{1}{4}$ etc. might be useful!
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

jagdish
Posts: 38
Joined: Wed Jan 19, 2011 2:21 pm
Location: India (Himanchal Pradesh)

Re: System of equations.

Unread post by jagdish » Thu Jan 12, 2012 9:17 pm

Thanks Admin Got it
jagdish

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