有关分式的急!1.已知A²-3A+1=0,试求（A²-A²分之1）（A-A分之1）2.已知：2分之X=3分之Y=4分之Z,求X²+Y²+Z²分之XY+2YZ-3XZ

Question

有关分式的急!
1.已知A²-3A+1=0,试求（A²-A²分之1）（A-A分之1）
2.已知：2分之X=3分之Y=4分之Z,求X²+Y²+Z²分之XY+2YZ-3XZ

Answer 1

A²-3A+1=0
A+1/A-3=0
A+1/A=3
A²+1/A²+2=9
A²+1/A²=7
（A²-A²分之1）（A-A分之1）
=(A+1/A)(A-1/A)²
=(A+1/A)(A²+1/A²-2)
=3*(7-2)
=3*5
=15
2、令x/2=y/3=z/4=t
x=2t
y=3y
z=4t
(XY+2YZ-3XZ)/(X²+Y²+Z²)
=(6t²+24t²-24t²)/(4t²+9t²+16t²)
=6/29