# Difference between revisions of "2014 UMO Problems/Problem 5"

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Find all positive real numbers <math>x, y</math>, and <math>z</math> that satisfy both of the following equations. | Find all positive real numbers <math>x, y</math>, and <math>z</math> that satisfy both of the following equations. | ||

− | < | + | <cmath> |

− | x^2 + y^2 + z^2 & = 4x\sqrt{yz}- 2yz \end{align*}</ | + | \begin{align*} xyz & = 1\\ |

− | + | x^2 + y^2 + z^2 & = 4x\sqrt{yz}- 2yz \end{align*} | |

+ | </cmath> | ||

== Solution == | == Solution == |