Difference between revisions of "1961 IMO Problems"

(Problem 1)
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==Day I==
 
==Day I==
 
===Problem 1===
 
===Problem 1===
 +
(''Hungary'')
 +
Solve the system of equations:
  
[[1961 IMO Problems/Problem 1 | Solution]]
+
<center>
 +
<math>
 +
\begin{matrix}
 +
\quad x + y + z \!\!\! &= a \; \, \\
 +
x^2 +y^2+z^2 \!\!\! &=b^2 \\
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\qquad \qquad xy \!\!\!  &= z^2
 +
\end{matrix}
 +
</math>
 +
</center>
  
 +
where <math>a </math> and <math>b </math> are constants.  Give the conditions that <math>a </math> and <math>b </math> must satisfy so that <math>x, y, z </math> (the solutions of the system) are distinct positive numbers.
  
 +
[[1961 IMO Problems/Problem 1 | Solution]]
  
 
===Problem 2===
 
===Problem 2===

Revision as of 11:29, 12 October 2007

Day I

Problem 1

(Hungary) Solve the system of equations:

$\begin{matrix} \quad x + y + z \!\!\! &= a \; \, \\ x^2 +y^2+z^2 \!\!\! &=b^2 \\ \qquad \qquad xy \!\!\!  &= z^2 \end{matrix}$

where $a$ and $b$ are constants. Give the conditions that $a$ and $b$ must satisfy so that $x, y, z$ (the solutions of the system) are distinct positive numbers.

Solution

Problem 2

Solution


Problem 3

Solution


Day 2

Problem 4

Solution


Problem 5

Solution


Problem 6

Solution



See Also

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