Question
Solve: .
Answer :
Word Count : 124
Given [ \frac{dx}{y^{2}+yz+z^{2}}=\frac{dy}{z^{2}+zx+x^{2}}=\frac{dz}{x^{2}+xy+y^{2}}. ] Because the system is completely symmetric in (x,y,z), first observe that taking [ x=y=z ] makes __________ _______ ____ ___ ________.
__________ ___ ____ ___ _______ ______ ________ ____ ______ ________ _______.
_______ ________ __________ _______ ____ ________ ___ _______ _____.
_________ _______ ______ ______ __________ ______ ___ _____.
_________ ______ ___ ________ ___ __________.
____ ____ ________ _______ ___ ________ ___ _______ _________ ___.
____ ____ ___ ______ __________.
______ ________ _________ ____ _____.
___ _________ _______ ________ _______ ______ _________ _________ __________ ______.
______ ____ _____ _____ _____ __________ ____.
___ __________ __________ ___ ____ ________ ___ _________ ________ __________.
_________ ______ ________ ________ __________ ______ _______ _____.
______ ____ ___ ________ __________ ________ __________ _______.
______ ___.
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Given [ \frac{dx}{y^{2}+yz+z^{2}}=\frac{dy}{z^{2}+zx+x^{2}}=\frac{dz}{x^{2}+xy+y^{2}}. ] Because the system is completely symmetric in (x,y,z), first observe that taking [ x=y=z ] makes __________ _______ ____ ___ ________.
__________ ___ ____ ___ _______ ______ ________ ____ ______ ________ _______.
_______ ________ __________ _______ ____ ________ ___ _______ _____.
_________ _______ ______ ______ __________ ______ ___ _____.
_________ ______ ___ ________ ___ __________.
____ ____ ________ _______ ___ ________ ___ _______ _________ ___.
____ ____ ___ ______ __________.
______ ________ _________ ____ _____.
___ _________ _______ ________ _______ ______ _________ _________ __________ ______.
______ ____ _____ _____ _____ __________ ____.
___ __________ __________ ___ ____ ________ ___ _________ ________ __________.
_________ ______ ________ ________ __________ ______ _______ _____.
______ ____ ___ ________ __________ ________ __________ _______.
______ ___.
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