y + z = -x( y + z )^5 = -x^5y^5 + 5y^4z + 10y^3z^2 + 10y^2z^3 + 5yz^4 + z^5 + x^5 = 0x^5 + y^5 + z^5 + 5yz(y^3 + 2y^2z + 2yz^2 + z^3 ) = 0x^5 + y^5 + z^5 + 5yz [(y + z )( y^2 - yz + z^2 ) + 2yz( y+z) ] = 0x^5 + y^5 + z^5 + 5yz ( y + z )( y^2 + yz + x^2 ) = 02( x^5 + y^5 + z^5 ) - 5xyz (( y^2 + 2yz + z^2 ) + y^2 + z^2 ) = 02( x^5 + y^5 + z^5 ) = 5xyz( x^2 + y^2 + x^2 )
y + z = -x
$( y + z )^5 = -x^5
$$y^5 + 5y^4z + 10y^3z^2 + 10y^2z^3 + 5yz^4 + z^5 + x^5 = 0
$$x^5 + y^5 + z^5 + 5yz(y^3 + 2y^2z + 2yz^2 + z^3 ) = 0
$$x^5 + y^5 + z^5 + 5yz [(y + z )( y^2 - yz + z^2 ) + 2yz( y+z) ] = 0
$$x^5 + y^5 + z^5 + 5yz ( y + z )( y^2 + yz + x^2 ) = 0
$$2( x^5 + y^5 + z^5 ) - 5xyz (( y^2 + 2yz + z^2 ) + y^2 + z^2 ) = 0
$$2( x^5 + y^5 + z^5 ) = 5xyz( x^2 + y^2 + x^2 )
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