已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x²-12xy+9y²/2x²-3xy

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 16:03:32
已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x²-12xy+9y²/2x²-3xy已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x&

已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x²-12xy+9y²/2x²-3xy
已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x²-12xy+9y²/2x²-3xy

已知2x+3y-5z=0,3x-2y+12z=0(z≠0),求4x²-12xy+9y²/2x²-3xy
2x+3y-5z=0,(1)
3x-2y+12z=0 (2)
(1)*12+(2)*5得:
(24+15)x+(36-10)y=0
39x+26y=0
3x=-2y
y/x=-3/2
4x²-12xy+9y²/2x²-3xy
=(2x-3y)²/[x(2x-3)]
=(2x-3y)/x
=2-3y/x
=2+9/2
=13/2

2x+3y-5z=0, (1)
3x-2y+12z=0 (2)
(1)*12+(2)*5得:
(24+15)x+(36-10)y=0
得 3x=-2y
4x²-12xy+9y²/2x²-3xy
=(2x-3y)²/[x(2x-3)]
=3/2

由已知式得2x+3y=5z,3x-2y=-12z
进而可求得x=-2z,y=3z
将上述关系式代入要求式得(2x*2-3xy)/(4x*2-12xy+9y*2)=(8z*2+18z*2) /(16z*2+72z*2+81z*2)=(26z*2)/(169z*2)=26/169