已知14(XX+YY+ZZ)=(X+2Y+3Z)^2,求X:Y:Z

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已知14(XX+YY+ZZ)=(X+2Y+3Z)^2,求X:Y:Z

已知14(XX+YY+ZZ)=(X+2Y+3Z)^2,求X:Y:Z
已知14(XX+YY+ZZ)=(X+2Y+3Z)^2,求X:Y:Z

已知14(XX+YY+ZZ)=(X+2Y+3Z)^2,求X:Y:Z
X:Y:Z=1:2:3
因为:14(XX+YY+ZZ)=(X+2Y+3Z)^2
14(XX+YY+ZZ)-(X+2Y+3Z)^2=0
13X^2+10Y^2+5Z^2-4XY-6XZ-12YZ=0
(4X^2-4XY+Y^2)+(9X^2-6XZ+Z^2)+(9Y^2-12YZ+4Z^2)=0
(2X-Y)^2+(3X-Z)^2+(3Y-2Z)^2=0
所以2X-Y=0,3X-Z=0,3Y-2Z=0
X:Y=1:2,X:Z=1:3,Y:Z=2:3
所以X:Y:Z=1:2:3