Question

若xyz≠0,且满足(y+z)/x=(x+z)/y=(x+y)/z,求[(y+z)(x+z)(x+y)]/xyz的值.

Answer 1

令a=(y+z)/x=(x+z)/y=(x+y)/z

y+z=ax

x+z=ay

x+y=az

相加

2(x+y+z)=a(x+y+z)

(a-2)(x+y+z)=0

a=2或x+y+z=0

则x+y=-z

a=(x+y)/z=-1

所以a=2或-1

所以原式=(ax)(ay)(az)/xyz

=a³

=8或-1