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1961 IMO Problems/Problem 1

Revision as of 15:53, 6 April 2007 by Teki-Teki (talk | contribs)
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Solve the following system of equations:

$x + y + z = a$

$x^2$$+y^2+z^2=b^2$

$xy = z^2$

where a and b are given real numbers. What conditions must hold on a and b for the solutions to be positive and distinct?

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