已知x/2=y/3=z/5 求x*x-y*y-z*z/xy-xz-yz=_____

题目

已知x/2=y/3=z/5 求x*x-y*y-z*z/xy-xz-yz=_____

答案

令a=x/2=y/3=z/5
则x=2a
y=3a
z=5a
所以x²=4a²
y²=9a²
z²=25a²
xy=6a²
xz=10a²
yz=15a²
所以原式=(4a²-9a²-25a²)/(6a²-10a²-15a²)
=-30a²/(-19a²)
=30/19