Question

(x+y)/3=(y+z)/5=(z+x)/4 ,xyz不等于0,求x:y:z

Answer 1

令(x+y)/3=(y+z)/5+(z+x)/4=k

所以x+y=3k (1)

y+z=5k (2)

z+x=4k (3)

相加

2(x+y+z)=12k

x+y+z=6k (4)

用(4)分别减去(1)(2)(3)

z=3k,x=k,y=2k

所以x:y:z=1:2:3