Question

若xyz不等于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

设(y+z)/x=(x+z)/y=(x+y)/z=k;

y+z=kx;x+z=ky;y+z=kx;

2(x+y+z)=k(x+y+z);

k=2或x+y+z=0;

所以,(y+z)(x+z)(x+y)/xyz=8或-1