已知x(y+z)/27=y(x+z)/32=z(x+y)/35,求z^2/x^2+y^2

令x(y+z)/27=y(x+z)/32=z(x+y)/35=k
xy+xz=27k
xy+yz=32k
xz+yz=35k
相加
2(xy+yz+zx)=94k
xy+yz+zx=47k
分别减去xy+xz=27k
xy+yz=32k
xz+yz=35k
yz=20k,zx=15k,xy=12k
y=20k/z,x=15k/z
xy=300k^2/z^2=12k
25k/z^2=1
z^2=25k
y=20k/z,
y^2=400k^2/z^2=16k
x=15k/z,
x^2=225k^2/z^2=9k
所以z^2/(x^2+y^2)
=(25k)/(16k+9k)
=1